ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Determinante/Calcular determinante 01 - Determinante de una matriz 2x2 Calcular el determinante de la matriz «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»M«/mi»«mn»1«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>a</mi></mtd><mtd><mi>h</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="|" open="|"><mi>M1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>retropersonal</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>Muy_bien</mi><mo>,</mo><mo> </mo><mi>Felicitaciones</mi><mo>,</mo><mo> </mo><mi>Excelente</mi><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>retropersonal</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Muy_bien</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Determinante Determina el determinante de la matriz #m Recuerda la forma de obtener el determinante. Puedes utilizar el método por menores o la regla de Sarrus. 1.0000000 0.1000000 0 0 #sol <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>determinante</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>5</mn></mtd><mtd><mn>10</mn></mtd><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>10</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>281</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #sol </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Determinante/Determinante con parametro 04 - Determinante igual a 0 (2x2) para que valor de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#955;«/mi»«/math» la matriz «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»M«/mi»«mn»1«/mn»«/math» tiene determinante igual a 0

obs: Entregue su solución simplificada.

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

obs: Entregue su solución simplificada.

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

"La matriz #M1 es invertibles" es...

]]> 1.0000000 1.0000000 0 Verdadero #retropersonal

]]> Falso Recuerda que una matriz es invertible cuando dicha matriz tiene inversa (lo que es equivalente a que su determinante sea distinto de cero)

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

obs: Entregue su solución simplificada.

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

obs: Entregue su solución simplificada.

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

A=#A

Encuentra la matriz inversa utilizando la fórmula de la matriz inversa vista en clase (es muy importante que recuerde la definición de la adjunta y no ingrese inmediatamente la formula de la inversa de 2x2):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»d«/mi»«mi»j«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»#A«/mi»«/math»=

{#1}	{#2}
{#3}	{#4}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mi»A«/mi»«mi»d«/mi»«mi»j«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»#A«/mi»«/mrow»«/mfenced»«mi»t«/mi»«/msup»«/math»=

{#5}	{#6}
{#7}	{#8}

|A|=

{#9}

A^-1=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mfenced close=¨|¨ open=¨|¨»«mi»A«/mi»«/mfenced»«/mfrac»«mi»A«/mi»«mi»d«/mi»«mi»j«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mo»(«/mo»«mi»A«/mi»«msup»«mo»)«/mo»«mi»t«/mi»«/msup»«mo»=«/mo»«/math»

{#10}	{#11}
{#12}	{#13}

A=#A

Encuentra la matriz inversa utilizando la fórmula de la matriz adjunta vista en clase:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»d«/mi»«mi»j«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»#A«/mi»«/math»=

{#1}	{#2}
{#3}	{#4}

{#5}	{#6}
{#7}	{#8}

|A|=

{#9}

{#10}	{#11}
{#12}	{#13}

A=#A

Encuentra la matriz inversa utilizando la fórmula de la matriz adjunta vista en clase:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»d«/mi»«mi»j«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»#A«/mi»«/math»=

{#1}	{#2}	{#3}
{#4}	{#5}	{#6}
{#7}	{#8}	{#9}

{#10}	{#11}	{#12}
{#13}	{#14}	{#15}
{#16}	{#17}	{#18}

|A|=

{#19}

{#20}	{#21}	{#22}
{#23}	{#24}	{#25}
{#26}	{#27}	{#28}

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close="&verbar;" open="&verbar;"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>32</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>24</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mn>21</mn></mtd><mtd><mn>24</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>28</mn></mtd><mtd><mn>21</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>168</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>1</mn><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></mfrac><mo>*</mo><mi>Aadj</mi></mrow></mfenced><mo>*</mo><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Encontrando la matriz inversa 3x3 con la matriz adjunta 2

A=#A

Encuentra la matriz inversa utilizando la fórmula de la matriz inversa vista en clase:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»d«/mi»«mi»j«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mi»#A«/mi»«/math»=

{#1}	{#2}	{#3}
{#4}	{#5}	{#6}
{#7}	{#8}	{#9}

{#10}	{#11}	{#12}
{#13}	{#14}	{#15}
{#16}	{#17}	{#18}

|A|=

{#19}

{#20}	{#21}	{#22}
{#23}	{#24}	{#25}
{#26}	{#27}	{#28}

]]> 28.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>Aadj</mi><mo>=</mo><mi>matriz_adjunta</mi><mo>(</mo><mi>A</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>detA</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></mtd></mtr><mtr><mtd><mi>at</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>bt</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>ct</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>dt</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>et</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>ft</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>gt</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>ht</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>it</mi><mo>=</mo><msub><mi>Aadj</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>At</mi><mo>=</mo><mo>(</mo><mi>Aadj</mi><msup><mo>)</mo><mo>T</mo></msup></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>g1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>h1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>i1</mi><mo>=</mo><msub><mi>At</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>Ai</mi><mo>=</mo><mfrac><mn>1</mn><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></mfrac><mo>*</mo><mi>Aadj</mi></mtd></mtr><mtr><mtd><mi>ai</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>bi</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>ci</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>di</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>ei</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>fi</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>gi</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>hi</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>ii</mi><mo>=</mo><msub><mi>Ai</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable><mrow><mfenced close="&verbar;" open="&verbar;"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Aadj</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>30</mn></mtd><mtd><mo>-</mo><mn>18</mn></mtd><mtd><mo>-</mo><mn>30</mn></mtd></mtr><mtr><mtd><mn>10</mn></mtd><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mo>-</mo><mn>13</mn></mtd></mtr><mtr><mtd><mn>16</mn></mtd><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mo>-</mo><mn>19</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>At</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>30</mn></mtd><mtd><mn>10</mn></mtd><mtd><mn>16</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>18</mn></mtd><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mo>-</mo><mn>9</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>30</mn></mtd><mtd><mo>-</mo><mn>13</mn></mtd><mtd><mo>-</mo><mn>19</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>1</mn><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></mfrac><mo>*</mo><mi>Aadj</mi></mrow></mfenced><mo>*</mo><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Inversa de una matriz/Metodo de Gauss Encontrando la matriz inversa 3x3 por el método de Gauss-Jordan 2

A=#AI

Resuelvelo utilizando el método de Gauss-Jordan realizando las operaciones que se te indican a continuación:

#a	#b	#c	#j	#M	#P
#d	#e	#f	#k	#N	#Q
#g	#h	#i	#l	#O	#R
{#1}	{#2}	{#3}	{#4}	{#5}	{#6}
{#7}	{#8}	{#9}	{#10}	{#11}	{#12}
{#13}	{#14}	{#15}	{#16}	{#17}	{#18}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mi»#w«/mi»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«mo»-«/mo»«mo»§nbsp;«/mo»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«/mrow»«/munder»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mi»#u«/mi»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#v«/mi»«mo»)«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»

{#19}	{#20}	{#21}	{#22}	{#23}	{#24}
{#25}	{#26}	{#27}	{#28}	{#29}	{#30}
{#31}	{#32}	{#33}	{#34}	{#35}	{#36}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«mi»#m«/mi»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#n«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«/mrow»«/munder»«/math»

{#37}	{#38}	{#39}	{#40}	{#41}	{#42}
{#43}	{#44}	{#45}	{#46}	{#47}	{#48}
{#49}	{#50}	{#51}	{#52}	{#53}	{#54}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«mfrac»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«mrow»«mi»#o«/mi»«/mrow»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«/mrow»«/munder»«/math»

{#55}	{#56}	{#57}	{#58}	{#59}	{#60}
{#61}	{#62}	{#63}	{#64}	{#65}	{#66}
{#67}	{#68}	{#69}	{#70}	{#71}	{#72}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#p«/mi»«mo»)«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»

{#73}	{#74}	{#75}	{#76}	{#77}	{#78}
{#79}	{#80}	{#81}	{#82}	{#83}	{#84}
{#85}	{#86}	{#87}	{#88}	{#89}	{#90}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#q«/mi»«mo»)«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»

{#91}	{#92}	{#93}	{#94}	{#95}	{#96}
{#97}	{#98}	{#99}	{#100}	{#101}	{#102}
{#103}	{#104}	{#105}	{#106}	{#107}	{#108}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«mfrac»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mi»#r«/mi»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»

{#109}	{#110}	{#111}	{#112}	{#113}	{#114}
{#115}	{#116}	{#117}	{#118}	{#119}	{#120}
{#121}	{#122}	{#123}	{#124}	{#125}	{#126}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#s«/mi»«mo»)«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»

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«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«mfrac»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mi»#t«/mi»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»

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{#157}	{#158}	{#159}	{#160}	{#161}	{#162}

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>=</mo><msub><mi>A3</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>N3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>O3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>R3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>3</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>A4</mi><mo>=</mo><mi>A3</mi></mtd></mtr><mtr><mtd><msub><mi>A4</mi><mn>3</mn></msub><mo>=</mo><mfrac><msub><mi>A4</mi><mn>3</mn></msub><mi>i3</mi></mfrac></mtd></mtr><mtr><mtd><mi>o</mi><mo>=</mo><mi>i3</mi></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>g4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>h4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>i4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>j4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>k4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>l4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>M4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>N4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>O4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>Q4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>R4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>3</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>A5</mi><mo>=</mo><mi>A4</mi></mtd></mtr><mtr><mtd><msub><mi>A5</mi><mn>2</mn></msub><mo>=</mo><msub><mi>A5</mi><mn>2</mn></msub><mo>-</mo><mi>f4</mi><mo>*</mo><msub><mi>A5</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>f4</mi></mtd></mtr><mtr><mtd><mi>a5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>g5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>h5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>i5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>j5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>k5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>l5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>M5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>N5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>O5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>Q5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>R5</mi><mo>=</mo><msub><mi>A5</mi><mrow><mn>3</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>A6</mi><mo>=</mo><mi>A5</mi></mtd></mtr><mtr><mtd><msub><mi>A6</mi><mn>1</mn></msub><mo>=</mo><msub><mi>A6</mi><mn>1</mn></msub><mo>-</mo><mi>c4</mi><mo>*</mo><msub><mi>A5</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>c4</mi></mtd></mtr><mtr><mtd><mi>a6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>g6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>h6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>i6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>j6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>k6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>l6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>M6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>N6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>O6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>Q6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>R6</mi><mo>=</mo><msub><mi>A6</mi><mrow><mn>3</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>A7</mi><mo>=</mo><mi>A6</mi></mtd></mtr><mtr><mtd><msub><mi>A7</mi><mn>2</mn></msub><mo>=</mo><mfrac><msub><mi>A7</mi><mn>2</mn></msub><mi>e6</mi></mfrac></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mi>e6</mi></mtd></mtr><mtr><mtd><mi>a7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>g7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>h7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>i7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>j7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>k7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>l7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>M7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>N7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>O7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>Q7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>R7</mi><mo>=</mo><msub><mi>A7</mi><mrow><mn>3</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>A8</mi><mo>=</mo><mi>A7</mi></mtd></mtr><mtr><mtd><msub><mi>A8</mi><mn>1</mn></msub><mo>=</mo><msub><mi>A8</mi><mn>1</mn></msub><mo>-</mo><mi>b7</mi><mo>*</mo><msub><mi>A8</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>b7</mi></mtd></mtr><mtr><mtd><mi>a8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>g8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>h8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>i8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>j8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>k8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>l8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>M8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>N8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>O8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>Q8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>R8</mi><mo>=</mo><msub><mi>A8</mi><mrow><mn>3</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>A9</mi><mo>=</mo><mi>A8</mi></mtd></mtr><mtr><mtd><msub><mi>A9</mi><mn>1</mn></msub><mo>=</mo><mfrac><msub><mi>A9</mi><mn>1</mn></msub><mi>a8</mi></mfrac></mtd></mtr><mtr><mtd><mi>t</mi><mo>=</mo><mi>a8</mi></mtd></mtr><mtr><mtd><mi>a9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>g9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>h9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>i9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>j9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>k9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>l9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>M9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>N9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>O9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>Q9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>2</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>R9</mi><mo>=</mo><msub><mi>A9</mi><mrow><mn>3</mn><mo>,</mo><mn>6</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>ecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi></mtd></mtr><mtr><mtd><mi>ecu2</mi><mo>=</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>z</mi></mtd></mtr><mtr><mtd><mi>ecu3</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>i</mi><mo>*</mo><mi>z</mi></mtd></mtr></mtable><mrow><mi>rango</mi><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>3</mn><mo>∧</mo><mi>h1</mi><mo>*</mo><mi>i1</mi><mo>*</mo><mi>e2</mi><mo>*</mo><mi>f2</mi><mo>*</mo><mi>m</mi><mo>*</mo><mi>n</mi><mo>*</mo><mi>o</mi><mo>*</mo><mi>p</mi><mo>*</mo><mi>q</mi><mo>*</mo><mi>r</mi><mo>*</mo><mi>s</mi><mo>*</mo><mi>t</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>o</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>r</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>t</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>j</mi></mtd><mtd><mi>M</mi></mtd><mtd><mi>P</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd><mtd><mi>k</mi></mtd><mtd><mi>N</mi></mtd><mtd><mi>Q</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd><mtd><mi>l</mi></mtd><mtd><mi>O</mi></mtd><mtd><mi>R</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>14</mn></mtd><mtd><mo>-</mo><mn>10</mn></mtd><mtd><mn>8</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>16</mn></mtd><mtd><mn>11</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>*</mo><mi>R33</mi><mo>-</mo><mi>X</mi><mo>*</mo><mi>R11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>R11</mi><mo>+</mo><mn>7</mn><mo>*</mo><mi>R33</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a1</mi></mtd><mtd><mi>b1</mi></mtd><mtd><mi>c1</mi></mtd><mtd><mi>j1</mi></mtd><mtd><mi>M1</mi></mtd><mtd><mi>P1</mi></mtd></mtr><mtr><mtd><mi>d1</mi></mtd><mtd><mi>e1</mi></mtd><mtd><mi>f1</mi></mtd><mtd><mi>k1</mi></mtd><mtd><mi>N1</mi></mtd><mtd><mi>Q1</mi></mtd></mtr><mtr><mtd><mi>g1</mi></mtd><mtd><mi>h1</mi></mtd><mtd><mi>i1</mi></mtd><mtd><mi>l1</mi></mtd><mtd><mi>O1</mi></mtd><mtd><mi>R1</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>14</mn></mtd><mtd><mo>-</mo><mn>10</mn></mtd><mtd><mn>8</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>117</mn></mtd><mtd><mn>37</mn></mtd><mtd><mn>8</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>7</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>*</mo><mi>R22</mi><mo>-</mo><mi>v</mi><mo>*</mo><mi>R11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R11</mi><mo>+</mo><mi>R22</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a2</mi></mtd><mtd><mi>b2</mi></mtd><mtd><mi>c2</mi></mtd><mtd><mi>j2</mi></mtd><mtd><mi>M2</mi></mtd><mtd><mi>P2</mi></mtd></mtr><mtr><mtd><mi>d2</mi></mtd><mtd><mi>e2</mi></mtd><mtd><mi>f2</mi></mtd><mtd><mi>k2</mi></mtd><mtd><mi>N2</mi></mtd><mtd><mi>Q2</mi></mtd></mtr><mtr><mtd><mi>g2</mi></mtd><mtd><mi>h2</mi></mtd><mtd><mi>i2</mi></mtd><mtd><mi>l2</mi></mtd><mtd><mi>O2</mi></mtd><mtd><mi>R2</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>17</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>117</mn></mtd><mtd><mn>37</mn></mtd><mtd><mn>8</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>7</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>*</mo><mi>R33</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>R22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>117</mn><mo>*</mo><mi>R22</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>R33</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a3</mi></mtd><mtd><mi>b3</mi></mtd><mtd><mi>c3</mi></mtd><mtd><mi>j3</mi></mtd><mtd><mi>M3</mi></mtd><mtd><mi>P3</mi></mtd></mtr><mtr><mtd><mi>d3</mi></mtd><mtd><mi>e3</mi></mtd><mtd><mi>f3</mi></mtd><mtd><mi>k3</mi></mtd><mtd><mi>N3</mi></mtd><mtd><mi>Q3</mi></mtd></mtr><mtr><mtd><mi>g3</mi></mtd><mtd><mi>h3</mi></mtd><mtd><mi>i3</mi></mtd><mtd><mi>l3</mi></mtd><mtd><mi>O3</mi></mtd><mtd><mi>R3</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>17</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>2174</mn></mtd><mtd><mn>157</mn></mtd><mtd><mn>117</mn></mtd><mtd><mn>35</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>R33</mi><mi>o</mi></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2174</mn></mfrac><mo>*</mo><mi>R33</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a4</mi></mtd><mtd><mi>b4</mi></mtd><mtd><mi>c4</mi></mtd><mtd><mi>j4</mi></mtd><mtd><mi>M4</mi></mtd><mtd><mi>P4</mi></mtd></mtr><mtr><mtd><mi>d4</mi></mtd><mtd><mi>e4</mi></mtd><mtd><mi>f4</mi></mtd><mtd><mi>k4</mi></mtd><mtd><mi>N4</mi></mtd><mtd><mi>Q4</mi></mtd></mtr><mtr><mtd><mi>g4</mi></mtd><mtd><mi>h4</mi></mtd><mtd><mi>i4</mi></mtd><mtd><mi>l4</mi></mtd><mtd><mi>O4</mi></mtd><mtd><mi>R4</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>17</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mfrac><mn>157</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>117</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>35</mn><mn>2174</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R22</mi><mo>-</mo><mi>p</mi><mo>*</mo><mi>R33</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R22</mi><mo>-</mo><mn>17</mn><mo>*</mo><mi>R33</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a5</mi></mtd><mtd><mi>b5</mi></mtd><mtd><mi>c5</mi></mtd><mtd><mi>j5</mi></mtd><mtd><mi>M5</mi></mtd><mtd><mi>P5</mi></mtd></mtr><mtr><mtd><mi>d5</mi></mtd><mtd><mi>e5</mi></mtd><mtd><mi>f5</mi></mtd><mtd><mi>k5</mi></mtd><mtd><mi>N5</mi></mtd><mtd><mi>Q5</mi></mtd></mtr><mtr><mtd><mi>g5</mi></mtd><mtd><mi>h5</mi></mtd><mtd><mi>i5</mi></mtd><mtd><mi>l5</mi></mtd><mtd><mi>O5</mi></mtd><mtd><mi>R5</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mfrac><mn>495</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>185</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>595</mn><mn>2174</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mfrac><mn>157</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>117</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>35</mn><mn>2174</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R11</mi><mo>-</mo><mi>q</mi><mo>*</mo><mi>R33</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R11</mi><mo>-</mo><mn>9</mn><mo>*</mo><mi>R33</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a6</mi></mtd><mtd><mi>b6</mi></mtd><mtd><mi>c6</mi></mtd><mtd><mi>j6</mi></mtd><mtd><mi>M6</mi></mtd><mtd><mi>P6</mi></mtd></mtr><mtr><mtd><mi>d6</mi></mtd><mtd><mi>e6</mi></mtd><mtd><mi>f6</mi></mtd><mtd><mi>k6</mi></mtd><mtd><mi>N6</mi></mtd><mtd><mi>Q6</mi></mtd></mtr><mtr><mtd><mi>g6</mi></mtd><mtd><mi>h6</mi></mtd><mtd><mi>i6</mi></mtd><mtd><mi>l6</mi></mtd><mtd><mi>O6</mi></mtd><mtd><mi>R6</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>0</mn></mtd><mtd><mfrac><mn>761</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>1053</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>315</mn><mn>2174</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mfrac><mn>495</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>185</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>595</mn><mn>2174</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mfrac><mn>157</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>117</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>35</mn><mn>2174</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>R22</mi><mi>r</mi></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>R22</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a7</mi></mtd><mtd><mi>b7</mi></mtd><mtd><mi>c7</mi></mtd><mtd><mi>j7</mi></mtd><mtd><mi>M7</mi></mtd><mtd><mi>P7</mi></mtd></mtr><mtr><mtd><mi>d7</mi></mtd><mtd><mi>e7</mi></mtd><mtd><mi>f7</mi></mtd><mtd><mi>k7</mi></mtd><mtd><mi>N7</mi></mtd><mtd><mi>Q7</mi></mtd></mtr><mtr><mtd><mi>g7</mi></mtd><mtd><mi>h7</mi></mtd><mtd><mi>i7</mi></mtd><mtd><mi>l7</mi></mtd><mtd><mi>O7</mi></mtd><mtd><mi>R7</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>0</mn></mtd><mtd><mfrac><mn>761</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>1053</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>315</mn><mn>2174</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mfrac><mn>99</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>37</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>119</mn><mn>2174</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mfrac><mn>157</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>117</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>35</mn><mn>2174</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R11</mi><mo>-</mo><mi>s</mi><mo>*</mo><mi>R22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R11</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>R22</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a8</mi></mtd><mtd><mi>b8</mi></mtd><mtd><mi>c8</mi></mtd><mtd><mi>j8</mi></mtd><mtd><mi>M8</mi></mtd><mtd><mi>P8</mi></mtd></mtr><mtr><mtd><mi>d8</mi></mtd><mtd><mi>e8</mi></mtd><mtd><mi>f8</mi></mtd><mtd><mi>k8</mi></mtd><mtd><mi>N8</mi></mtd><mtd><mi>Q8</mi></mtd></mtr><mtr><mtd><mi>g8</mi></mtd><mtd><mi>h8</mi></mtd><mtd><mi>i8</mi></mtd><mtd><mi>l8</mi></mtd><mtd><mi>O8</mi></mtd><mtd><mi>R8</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mfrac><mn>133</mn><mn>1087</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>434</mn><mn>1087</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>455</mn><mn>1087</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mfrac><mn>99</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>37</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>119</mn><mn>2174</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mfrac><mn>157</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>117</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>35</mn><mn>2174</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>R33</mi><mi>t</mi></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>14</mn></mfrac><mo>*</mo><mi>R33</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a9</mi></mtd><mtd><mi>b9</mi></mtd><mtd><mi>c9</mi></mtd><mtd><mi>j9</mi></mtd><mtd><mi>M9</mi></mtd><mtd><mi>P9</mi></mtd></mtr><mtr><mtd><mi>d9</mi></mtd><mtd><mi>e9</mi></mtd><mtd><mi>f9</mi></mtd><mtd><mi>k9</mi></mtd><mtd><mi>N9</mi></mtd><mtd><mi>Q9</mi></mtd></mtr><mtr><mtd><mi>g9</mi></mtd><mtd><mi>h9</mi></mtd><mtd><mi>i9</mi></mtd><mtd><mi>l9</mi></mtd><mtd><mi>O9</mi></mtd><mtd><mi>R9</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mfrac><mn>19</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>31</mn><mn>1087</mn></mfrac></mtd><mtd><mfrac><mn>65</mn><mn>2174</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mfrac><mn>99</mn><mn>2174</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>37</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>119</mn><mn>2174</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mfrac><mn>157</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>117</mn><mn>2174</mn></mfrac></mtd><mtd><mfrac><mn>35</mn><mn>2174</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Matriz inversa 2x2 por el método de Gauss-Jordan Si A= #AI Utiliza el método de Gauss-Jordan para encontrar la matriz inversa de la matriz A realizando las operaciones sugeridas:

	#a	#b	#e	#g
	#c	#d	#f	#h
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mo»(«/mo»«mi»#d«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»-«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#b«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»	{#1}	{#2}	{#3}	{#4}
	{#5}	{#6}	{#7}	{#8}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mfrac»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mi»#q«/mi»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»	{#9}	{#10}	{#11}	{#12}
	{#13}	{#14}	{#15}	{#16}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#c«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»	{#17}	{#18}	{#19}	{#20}
	{#21}	{#22}	{#23}	{#24}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mrow»«mi»#d«/mi»«/mrow»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/math»	{#25}	{#26}	{#27}	{#28}
	{#29}	{#30}	{#31}	{#32}

]]> 32.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi></mtd></mtr></mtable><mrow><mfenced close="&verbar;" open="&verbar;"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>b</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>c</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>d</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>q</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AI</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>=</mo><mi>A</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A2</mi><mo>=</mo><mi>A1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A2</mi><mn>1</mn></msub><mo>=</mo><mfrac><msub><mi>A2</mi><mn>1</mn></msub><mi>q</mi></mfrac></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>h2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A3</mi><mo>=</mo><mi>A2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A3</mi><mn>2</mn></msub><mo>=</mo><msub><mi>A3</mi><mn>2</mn></msub><mo>-</mo><mi>c</mi><mo>*</mo><msub><mi>A3</mi><mn>1</mn></msub></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>*</mo><mfenced><mtable><mtr><mtd><mi>e4</mi></mtd><mtd><mi>g4</mi></mtd></mtr><mtr><mtd><mi>f4</mi></mtd><mtd><mi>h4</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Matriz inversa 2x2 por el método de Gauss-Jordan 2 Si A= #AI Utiliza el método de Gauss-Jordan para encontrar la matriz inversa de la matriz A realizando las operaciones sugeridas:

	#a	#b	#e	#g
	#c	#d	#f	#h
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mo»(«/mo»«mi»#d«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»-«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#b«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»	{#1}	{#2}	{#3}	{#4}
	{#5}	{#6}	{#7}	{#8}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mfrac»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mi»#q«/mi»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»	{#9}	{#10}	{#11}	{#12}
	{#13}	{#14}	{#15}	{#16}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#c«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»	{#17}	{#18}	{#19}	{#20}
	{#21}	{#22}	{#23}	{#24}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mrow»«mi»#d«/mi»«/mrow»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/math»	{#25}	{#26}	{#27}	{#28}
	{#29}	{#30}	{#31}	{#32}

]]> 32.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi></mtd></mtr></mtable><mrow><mfenced close="&verbar;" open="&verbar;"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>b</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>c</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>d</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>q</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi><mo>=</mo><msub><mi>A1</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A2</mi><mo>=</mo><mi>A1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A2</mi><mn>1</mn></msub><mo>=</mo><mfrac><msub><mi>A2</mi><mn>1</mn></msub><mi>q</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h2</mi><mo>=</mo><msub><mi>A2</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A3</mi><mo>=</mo><mi>A2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A3</mi><mn>2</mn></msub><mo>=</mo><msub><mi>A3</mi><mn>2</mn></msub><mo>-</mo><mi>c</mi><mo>*</mo><msub><mi>A3</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h3</mi><mo>=</mo><msub><mi>A3</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A4</mi><mo>=</mo><mi>A3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A4</mi><mn>2</mn></msub><mo>=</mo><mfrac><msub><mi>A4</mi><mn>2</mn></msub><mi>d</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>c4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>e4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>f4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h4</mi><mo>=</mo><msub><mi>A4</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>8</mn></mtd><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>40</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>8</mn></mtd><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mfrac><mn>3</mn><mn>20</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>1</mn><mn>20</mn></mfrac></mtd></mtr><mtr><mtd><mo>-</mo><mn>8</mn></mtd><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mfrac><mn>3</mn><mn>20</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>1</mn><mn>20</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mo>-</mo><mfrac><mn>6</mn><mn>5</mn></mfrac></mtd><mtd><mfrac><mn>3</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mfrac><mn>3</mn><mn>20</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>1</mn><mn>20</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>1</mn><mn>10</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>*</mo><mfenced><mtable><mtr><mtd><mi>e4</mi></mtd><mtd><mi>g4</mi></mtd></mtr><mtr><mtd><mi>f4</mi></mtd><mtd><mi>h4</mi></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Operatoria de Matrices Rango de una matriz Determina el rango de la matriz #M . Recuerda que el rango de una matriz es el número de renglones de la matriz que son linealmente independientes. 1.0000000 0.1000000 0 true true abc Revisa tu respuesta, recuerda bien la definición del rango de una matriz. #sol Muy bien , lo lograste. #a #b #c <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>rango</mi><mo>(</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>/</mo><mo>{</mo><mi>sol</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>L</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msub><mi>L</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msub><mi>L</mi><mn>3</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> U1 Matrices: Producto teoría Sean las matrices:

A=#A

B=#B

C=#C

Indica, respondiendo SI o NO en el recuadro (es importante que lo escribas en mayúsculas), si se pueden realizar los productos que se indican.

En caso que sí se puedan multiplicar, indica en los siguientes recuadros las dimensiones de la matriz producto.

Si no se pueden multiplicar, introduce el número 0 en los 2 recuadros de las dimensiones.

1) A·B

¿Se pueden multiplicar? {#1}

¿Cuales son las dimensiones de la matriz producto? {#2}x{#3}

2) B·A

¿Se pueden multiplicar? {#4}

¿Cuales son las dimensiones de la matriz producto? {#5}x{#6}

3) A·C

¿Se pueden multiplicar? {#7}

¿Cuales son las dimensiones de la matriz producto? {#8}x{#9}

4) C·A

¿Se pueden multiplicar? {#10}

¿Cuales son las dimensiones de la matriz producto? {#11}x{#12}

5) B·C

¿Se pueden multiplicar? {#13}

¿Cuales son las dimensiones de la matriz producto? {#14}x{#15}

6) C·B

¿Se pueden multiplicar? {#16}

¿Cuales son las dimensiones de la matriz producto? {#17}x{#18}

7) A·A=A²

¿Se pueden multiplicar? {#19}

¿Cuales son las dimensiones de la matriz producto? {#20}x{#21}

8) B·B=B²

¿Se pueden multiplicar? {#22}

¿Cuales son las dimensiones de la matriz producto? {#23}x{#24}

9) C·C=C²

¿Se pueden multiplicar? {#25}

¿Cuales son las dimensiones de la matriz producto? {#26}x{#27}

]]> 27.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>A</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>A</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>5</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>6</mn></mrow><mrow><mi>A</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>7</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>8</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>9</mn></mrow><mrow><mi>A</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>10</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>11</mn></mrow><mrow><mi>A</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>12</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>13</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>14</mn></mrow><mrow><mi>A</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>15</mn></mrow><mrow><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ii</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>B</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>B</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>5</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>6</mn></mrow><mrow><mi>B</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>7</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>8</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>9</mn></mrow><mrow><mi>B</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>10</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>11</mn></mrow><mrow><mi>B</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>12</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>13</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>14</mn></mrow><mrow><mi>B</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ii</mi><mo>=</mo><mn>15</mn></mrow><mrow><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iii</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>C</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>C</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>5</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>6</mn></mrow><mrow><mi>C</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>7</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>8</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>9</mn></mrow><mrow><mi>C</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>10</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>11</mn></mrow><mrow><mi>C</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>12</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>13</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>14</mn></mrow><mrow><mi>C</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>iii</mi><mo>=</mo><mn>15</mn></mrow><mrow><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm1</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd11</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd12</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm1</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd11</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd12</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm2</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd21</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd22</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm2</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd21</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd22</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm3</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd31</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd32</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm3</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd31</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd32</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm4</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd41</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd42</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm4</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd41</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd42</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm5</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd51</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd52</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm5</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd51</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd52</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm6</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd61</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd62</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm6</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd61</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd62</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm7</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd71</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd72</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>A</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm7</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd71</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd72</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm8</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd81</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd82</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>B</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm8</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd81</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd82</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n_columnas</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>rm9</mi><mo>=</mo><mo>"</mo><mi>SI</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd91</mi><mo>=</mo><mi>n_filas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>rd92</mi><mo>=</mo><mi>n_columnas</mi><mo>(</mo><mi>C</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>rm9</mi><mo>=</mo><mo>"</mo><mi>NO</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd91</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr><mtr><mtd><mi>rd92</mi><mo>=</mo><mo>"</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>5</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>6</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>6</mn></mtd><mtd><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>SI</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>NO</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>NO</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd31</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd32</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>SI</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd41</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>NO</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd51</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd52</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>NO</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd61</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rd62</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_string"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Operatoria de Matrices/Basica (suma y productos) 01 - SUMA DE MATRICES Determine el resultado de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»M«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»M«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

obs: Trabaja con valores exactos

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

obs:trabaja con valores exactos

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mfrac><mrow><mi>l</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mfrac><mrow><mi>l</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mi>r</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mfrac><mrow><mi>r</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mi>r</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mfrac><mrow><mi>l</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>M1</mi><mo>=</mo><mi>A</mi></mrow><mrow><mi>M2</mi><mo>=</mo><mi>C</mi></mrow><mrow><mi>M2</mi><mo>=</mo><mi>D</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>M1</mi><mo>*</mo><mi>M2</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Retroalimentación</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>retropersonal</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>"</mo><mi>Bien</mi><mo>.</mo><mo> </mo><mi>Continúa</mi><mo> </mo><mi>de</mi><mo> </mo><mi>esa</mi><mo> </mo><mi>manera</mi><mo>.</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>¡</mo><mi>Muy</mi><mo> </mo><mi>bien</mi><mo>!</mo><mo> </mo><mi>Sigue</mi><mo> </mo><mi>así</mi><mo>.</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>¡</mo><mi>Excelente</mi><mo>!</mo><mo>"</mo><mo>,</mo><mo>"</mo><mi>Felicitaciones</mi><mo>,</mo><mo> </mo><mo>¡</mo><mi>muy</mi><mo> </mo><mi>bien</mi><mo>!</mo><mo>"</mo><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac></mtd><mtd><mo>-</mo><mn>7</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mfrac><mn>23</mn><mn>2</mn></mfrac></mtd><mtd><mo>-</mo><mn>6</mn></mtd></mtr><mtr><mtd><mfrac><mn>21</mn><mn>2</mn></mfrac></mtd><mtd><mfrac><mn>21</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 04 - MULTIPLICACIÓN DE MATRICES (no cuadradas) Determine el resultado de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»M«/mi»«mn»1«/mn»«mo»*«/mo»«mo»#«/mo»«mi»M«/mi»«mn»2«/mn»«/math»

obs:trabaja con valores exactos

]]> 1.0000000 0.3333333 0 0 #sol #retropersonal

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mfrac><mrow><mi>r</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd><mtd><mfrac><mrow><mi>l</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mfrac><mrow><mi>r</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mfrac><mrow><mi>l</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mfrac><mrow><mi>r</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mfrac><mrow><mi>r</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd><mtd><mfrac><mrow><mi>l</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></mfrac></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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</mo><mi>así</mi><mo>.</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>¡</mo><mi>Excelente</mi><mo>!</mo><mo>"</mo><mo>,</mo><mo>"</mo><mi>Felicitaciones</mi><mo>,</mo><mo> </mo><mo>¡</mo><mi>muy</mi><mo> </mo><mi>bien</mi><mo>!</mo><mo>"</mo><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mfrac><mn>7</mn><mn>2</mn></mfrac></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>16</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd><mtd><mn>8</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 07 - PRODUCTO DE MATRICES «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#183;«/mo»«mi»B«/mi»«/math», donde «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mi»#A«/mi»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mi»#B«/mi»«/math».]]> 1.0000000 0.1000000 0 0 #M ]]> <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>A</mi><mo>·</mo><mi>B</mi></math></input></command></group></library></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #M </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> U1 Matrices: Problema de matrices con dos parámetros

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»+«/mo»«mi»m«/mi»«mo»§#183;«/mo»«mi»A«/mi»«mo»+«/mo»«mi»n«/mi»«mo»§#183;«/mo»«mi»I«/mi»«mo»=«/mo»«mn»0«/mn»«/math»

Siendo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»I«/mi»«/math» la matriz identidad correspondiente y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» la matriz nula correspondiente.

]]>

Al realizar los productos y sumas de la expresión A + m·A + n·I = 0, obtenemos la siguiente igualdad:

#P = #O

Resolvemos entonces las 4 ecuaciones:

#e1 = 0

#e2 = 0

#e3 = 0

#e4 = 0

Y obtenemos que: m = #m y n = #n.

]]> 1.0000000 0.1000000 0 0 m=#mn=#n]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>nn</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>i</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo></mtd></mtr><mtr><mtd><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>1</mn><mi>m</mi><mo>+</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></mtd><mtd><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>1</mn><mi>m</mi><mo>&quot;</mo><mo>,</mo><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>)</mo></mtd></mtr><mtr><mtd><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>1</mn><mi>m</mi><mo>&quot;</mo><mo>,</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></mtd><mtd><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>1</mn><mi>m</mi><mo>+</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn><mo>+</mo><mn>4</mn><ms>m</ms><mo>+</mo><ms>n</ms></mtd><mtd><mn>3</mn><mo>+</mo><mn>3</mn><ms>m</ms></mtd></mtr><mtr><mtd><mn>3</mn><mo>+</mo><mn>3</mn><ms>m</ms></mtd><mtd><mn>4</mn><mo>+</mo><mn>4</mn><ms>m</ms><mo>+</mo><ms>n</ms></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>+</mo><mi>m</mi><mo>·</mo><mi>A</mi><mo>+</mo><mi>n</mi><mo>·</mo><msub><ident definitionURL="http://www.wiris.com/XML/csymbol"/><mn>2</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>#m</mi><mspace linebreak="newline"/><mi>n</mi><mo>=</mo><mi>#n</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> U1 Matrices: Problema de matrices con dos parámetros 2

A = #A, B = #B, C = #C y D = #D

Encontrar los valores de x e y que verifican la ecuación: A·B + C = 2D.

Indica tu respuesta así:

]]>

Multiplicamos las matrices A·B y obtenemos #AB.

Le sumamos la matriz C y obtenemos: #ABC. Al igualar esta matriz a la matriz 2·D, nos quedan las siguientes ecuaciones:

#e1

#e2

Resolviendo este sistema de ecuaciones obtenemos los valores: x = #x, y = #y.

]]> 1.0000000 0.1000000 0 0 x=#xy=#y]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>]</mo><mo>=</mo><mo>[</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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y producto por número real 1 #expr

obs: I es la matriz identidad.

]]> 1.0000000 0.3333333 0 0 #M1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>s</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>t</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>l</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>M2</mi><mo>=</mo><mi>A</mi></mrow><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><msup><mi>M2</mi><mi>n</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>23</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>19</mn></mtd><mtd><mo>-</mo><mn>8</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>11</mn></mtd><mtd><mn>14</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#M1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 06 - EVALUAR MATRICES EN UN POLINOMIO (grado 2) Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»#«/mo»«mi»M«/mi»«mn»1«/mn»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mi»i«/mi»«/math», calcular el valor de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»A«/mi»«mo»)«/mo»«/math»

#mat

]]> 1.0000000 0.3333333 0 true true abc #sol

]]> #a

]]> #b

#mat

]]> 1.0000000 0.3333333 0 true true abc #sol

]]> #a

]]> #b

]]> #c

#mat

]]> 1.0000000 0.3333333 0 true true abc #sol

]]> #a

]]> #b

]]> #c

]]> <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mat</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>rang</mi><mo>(</mo><mi>mat</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>/</mo><mo>{</mo><mi>sol</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>L</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msub><mi>L</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msub><mi>L</mi><mn>3</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> U1 Matrices: Producto, Potencia 3.]]> 1.0000000 0.1000000 0 0 #sol <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>A</mi><mn>3</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>39</mn></mtd><mtd><mn>27</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Operatoria de Matrices/Transpuesta 08 RESOLVER EXPRESION Resuelva la siguiente expresión «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»A«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»B«/mi»«mo»+«/mo»«mi»A«/mi»«mo»§#183;«/mo»«mi»C«/mi»«/math», sabiendo que:

A=#A1, B=#B1 y C=#C1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>A1</mi><mo>=</mo><mi>X</mi></mrow><mtable><mtr><mtd><mi>B1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mn>0</mn></mtd><mtd><mi>a</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>C1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>b</mi></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>B1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>C1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mi>T</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>A</mi><mo>=</mo><mi>A</mi></mrow><mrow><mi>A</mi><mo>=</mo><msup><mi>A</mi><mi>T</mi></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>D</mi><mo>=</mo><mi>A1</mi></mrow><mrow><mi>D</mi><mo>=</mo><msup><mi>A1</mi><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mi>T</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>B</mi><mo>=</mo><mi>B</mi></mrow><mrow><mi>B</mi><mo>=</mo><msup><mi>B</mi><mi>T</mi></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>E</mi><mo>=</mo><mi>B1</mi></mrow><mrow><mi>E</mi><mo>=</mo><msup><mi>B1</mi><mo>T</mo></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>D</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>E</mi><mo>+</mo><mi>A1</mi><mo>*</mo><mi>C1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>15</mn></mtd><mtd><mo>-</mo><mn>15</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>15</mn></mtd><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 09 - RANGO DE UNA MATRIZ «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»M«/mi»«mo»=«/mo»«mi»#M«/mi»«/math», calcular su rango
]]> 1.0000000 0.1000000 0 0 #R <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mn>0</mn></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mn>0</mn></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>rank</mi><mfenced><mi>M</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#R</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> U1 Matrices: Producto ejercicio casa A=#A

B=#B

Calcular:

A^TA+2(B²+I)

obs: Recuerde que I es la matriz Identidad

obs: Recuerde que I es la matriz identidad

]]> 5.0000000 0.1000000 0 0 #sol <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AA</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BB</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>·</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>·</mo><mo>&quot;</mo><mo>,</mo><mi>a</mi><mo>·</mo><mi>A</mi><mo>+</mo><mi>i</mi><mo>·</mo><mi>I</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b</mi><mo>·</mo><msup><mi>BB</mi><mo>T</mo></msup><mo>+</mo><mi>a</mi><mo>·</mo><mi>AA</mi><mo>+</mo><mi>i</mi><mo>·</mo><msub><ident definitionURL="http://www.wiris.com/XML/csymbol"/><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BB</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>A</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>I</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><ms>·</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> U1 Matrices: Suma y producto por número real 3 #expr A^T]]> 5.0000000 0.1000000 0 0 #sol <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AA</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BB</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>·</mo><mo>&quot;</mo><mo>,</mo><mi>b</mi><mo>·</mo><mi>B</mi><mo>+</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>·</mo><msup><mi>AA</mi><mo>T</mo></msup><mo>+</mo><mi>b</mi><mo>·</mo><mi>BB</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BB</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>B</mi><mo>-</mo><mn>2</mn><ms>·</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>8</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>22</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>14</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> U1 Matrices: Suma y producto por número real 4 #expr B^T]]> 5.0000000 0.1000000 0 0 #sol <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AA</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BB</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>·</mo><mo>&quot;</mo><mo>,</mo><mi>a</mi><mo>·</mo><mi>A</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>AA</mi><mo>+</mo><mi>b</mi><mo>·</mo><msup><mi>BB</mi><mo>T</mo></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BB</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>A</mi><mo>-</mo><mn>2</mn><ms>·</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>9</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>10</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Propiedades y Matrices Especiales 01- MATRICES ESPECIALES ]]> 1.0000000 0.1000000 0 true #TS Triangular superior #TI Triangular inferior #D Diagonal #S Simétrica #AS Antisimétrica ]]> Identidad ]]> Escalar <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TS</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TI</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>g</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>e</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>h</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>i</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi></mtd><mtd><mi>a</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd></mtr><mtr><mtd><mi>f</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>g</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AS</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>g</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>g</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>e</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>b</mi></mtd><mtd><mo>-</mo><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><msub><ident definitionURL="http://www.wiris.com/XML/csymbol"/><mrow><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>a</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 02 - MATRICES IMPLICITAS Sean las matrices: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«/math» definida por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mrow»«mi»i«/mi»«mi»j«/mi»«/mrow»«/msub»«mo»=«/mo»«mo»#«/mo»«mi»i«/mi»«mi»m«/mi»«mi»p«/mi»«mi»l«/mi»«mn»1«/mn»«/math» con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«mo»§#8804;«/mo»«mi»i«/mi»«mo»§#8804;«/mo»«mn»3«/mn»«mo»;«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mo»§#8804;«/mo»«mi»j«/mi»«mo»§#8804;«/mo»«mn»3«/mn»«/math» y la matriz «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«/math» definida por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»b«/mi»«mrow»«mi»i«/mi»«mi»j«/mi»«/mrow»«/msub»«mo»=«/mo»«mo»#«/mo»«mi»i«/mi»«mi»m«/mi»«mi»p«/mi»«mi»l«/mi»«mn»2«/mn»«/math» con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«mo»§#8804;«/mo»«mi»i«/mi»«mo»§#8804;«/mo»«mn»3«/mn»«mo»;«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mo»§#8804;«/mo»«mi»j«/mi»«mo»§#8804;«/mo»«mn»3«/mn»«/math». Determine, explicitamente, el valor de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»+«/mo»«mi»B«/mi»«/math»

]]> 1.0000000 0.0000000 0 0 #sol Muy bien!! La respuesta correcta es #sol, donde A=#M1 y B=#M2

]]> *]]> Recuerde que en una matriz respresentada por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mrow»«mi»i«/mi»«mi»j«/mi»«/mrow»«/msub»«/math», primero debemos identificar de que tamaño es la matriz indicada. Luego, cada elemento se obtiene reemplazando i y j, donde i es la fila y j es la columna donde se encuentra dicho elemento. En nuestro caso, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mrow»«mi»i«/mi»«mi»j«/mi»«/mrow»«/msub»«mo»=«/mo»«mo»#«/mo»«mi»i«/mi»«mi»m«/mi»«mi»p«/mi»«mi»l«/mi»«mn»1«/mn»«/math» entonces (por ejemplo) el elemento «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mrow»«mn»12«/mn»«mo»=«/mo»«/mrow»«/msub»«/math»#retro1 porque i=1 y j=2. Debes Intentarlo nuevamente, ánimo!!

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>z</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>j</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>j</mi><mo>,</mo><msup><mi>i</mi><mi>j</mi></msup><mo>,</mo><msup><mi>j</mi><mi>i</mi></msup><mo>,</mo><mi>a</mi><mo>+</mo><mi>j</mi><mo>,</mo><mi>a</mi><mo>+</mo><mi>i</mi><mo>,</mo><mi>a</mi><mo>-</mo><mi>j</mi><mo>,</mo><mi>a</mi><mo>-</mo><mi>i</mi><mo>}</mo></mtd></mtr><mtr><mtd><mi>t</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>c</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>j</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>j</mi><mo>,</mo><msup><mi>i</mi><mi>j</mi></msup><mo>,</mo><msup><mi>j</mi><mi>i</mi></msup><mo>,</mo><mi>c</mi><mo>+</mo><mi>j</mi><mo>,</mo><mi>c</mi><mo>+</mo><mi>i</mi><mo>,</mo><mi>c</mi><mo>-</mo><mi>j</mi><mo>,</mo><mi>c</mi><mo>-</mo><mi>i</mi><mo>}</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>z</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>≠</mo><mi>t</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>impl1</mi><mo>=</mo><mi>z</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>impl2</mi><mo>=</mo><mi>t</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>retro1</mi><mo>=</mo><mi>z</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>z</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd><mtd><mi>z</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd><mtd><mi>z</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd><mtd><mi>z</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd><mtd><mi>z</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd><mtd><mi>z</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd><mtd><mi>z</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>t</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>t</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>t</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd><mtd><mi>t</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>M1</mi><mo>+</mo><mi>M2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>i</mi><mi>j</mi></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>j</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>impl1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>i</mi><mi>j</mi></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>impl2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>j</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>27</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mo>-</mo><mn>7</mn></mtd><mtd><mo>-</mo><mn>8</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mo>-</mo><mn>7</mn></mtd><mtd><mo>-</mo><mn>8</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mo>-</mo><mn>7</mn></mtd><mtd><mo>-</mo><mn>8</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mo>-</mo><mn>7</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>19</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>retro1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>*</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_all" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 03 - Transpuesta de la matriz

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»TM1«/mi»«mo»=«/mo»«mi»#BT«/mi»«/math» , «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»TM2«/mi»«mo»=«/mo»«mi»#CT«/mi»«/math» , «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»TM3«/mi»«mo»=«/mo»«mi»#AT«/mi»«/math»

]]> 1.0000000 0.1000000 0 true #B TM1 #C TM2 #A TM3 <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub></mtd><mtd><msub><mi>u</mi><mn>2</mn></msub></mtd><mtd><msub><mi>u</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>v</mi><mn>1</mn></msub></mtd><mtd><msub><mi>v</mi><mn>2</mn></msub></mtd><mtd><msub><mi>v</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>w</mi><mn>1</mn></msub></mtd><mtd><msub><mi>w</mi><mn>2</mn></msub></mtd><mtd><msub><mi>w</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo><mi>AT</mi><mo>=</mo><msup><mi>A</mi><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub></mtd><mtd><msub><mi>u</mi><mn>2</mn></msub></mtd><mtd><msub><mi>u</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>v</mi><mn>3</mn></msub></mtd><mtd><msub><mi>v</mi><mn>2</mn></msub></mtd><mtd><msub><mi>v</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><msub><mi>w</mi><mn>1</mn></msub></mtd><mtd><msub><mi>w</mi><mn>2</mn></msub></mtd><mtd><msub><mi>w</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo><mi>BT</mi><mo>=</mo><msup><mi>B</mi><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub></mtd><mtd><msub><mi>u</mi><mn>2</mn></msub></mtd><mtd><msub><mi>u</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>v</mi><mn>1</mn></msub></mtd><mtd><msub><mi>v</mi><mn>2</mn></msub></mtd><mtd><msub><mi>v</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>w</mi><mn>3</mn></msub></mtd><mtd><msub><mi>w</mi><mn>2</mn></msub></mtd><mtd><msub><mi>w</mi><mn>1</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo><mi>CT</mi><mo>=</mo><msup><mi>C</mi><mo>T</mo></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mi>AT</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mn>7</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>8</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mn>7</mn></mtd><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>6</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>,</mo><mi>BT</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mn>8</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>6</mn></mtd><mtd><mn>7</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>,</mo><mi>CT</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mn>7</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>8</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mn>7</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>6</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>8</mn></mtd></mtr></mtable></mfenced></math></output></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> 04 - Dimensión de una matriz n={#1}«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»×«/mo»«/math»m={#2}]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><pi/><mo>,</mo><exponentiale/><mo>,</mo><msqrt><mn>2</mn></msqrt><mo>,</mo><msqrt><mn>3</mn></msqrt><mo>,</mo><msqrt><mn>5</mn></msqrt><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>b</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>{</mo><mi>c</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>b</mi><mo>(</mo><mo>)</mo><mo>,</mo><mn>1</mn><mo>}</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dime</mi><mo>=</mo><mi>dimensiones</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><msub><mi>dime</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msub><mi>dime</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>j</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>m</mi></mrow><mrow><msub><msub><mi>A</mi><mi>i</mi></msub><mi>j</mi></msub><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></mrow></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>4</mn><mo>*</mo><pi/></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>10</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mtd></mtr><mtr><mtd><mn>36</mn></mtd><mtd><mo>-</mo><mn>8</mn></mtd><mtd><mfrac><mn>52</mn><mn>19</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>19</mn></mfrac></mtd></mtr><mtr><mtd><mn>91</mn></mtd><mtd><mfrac><mn>20</mn><mn>3</mn></mfrac></mtd><mtd><mo>-</mo><mn>4</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></mtd><mtd><mfrac><mrow><mn>5</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>8</mn></mfrac></mtd></mtr><mtr><mtd><mn>3</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></mtd><mtd><mo>-</mo><mfrac><mrow><mn>3</mn><mo>*</mo><pi/><mo>*</mo><msqrt><mn>5</mn></msqrt></mrow><mn>5</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>15</mn></mfrac></mtd><mtd><mfrac><mn>4</mn><mn>13</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 05 - Elementos de una matriz

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»_{1 #n1}={#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»_{2 #n2}={#2}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»_{#m1 #n3}={#3}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»_{#m2 #n4}={#4}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»_{#m3 #n5}={#5}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»_{#m4 #n6}={#6}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»_{#m5 #n7}={#7}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»_{#m6 #n8}={#8}

]]> 8.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>c</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>d</mi><mo>(</mo><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dime</mi><mo>=</mo><mi>dimensiones</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><msub><mi>dime</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msub><mi>dime</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>j</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>m</mi></mrow><mrow><msub><msub><mi>A</mi><mi>i</mi></msub><mi>j</mi></msub><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>re</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>co</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>re</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>re</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>re</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>re</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi><mo>=</mo><mi>re</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n6</mi><mo>=</mo><mi>re</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n7</mi><mo>=</mo><mi>re</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n8</mi><mo>=</mo><mi>re</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>co</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>co</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>=</mo><mi>co</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m4</mi><mo>=</mo><mi>co</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m5</mi><mo>=</mo><mi>co</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m6</mi><mo>=</mo><mi>co</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1n1</mi><mo>=</mo><msub><msub><mi>A</mi><mn>1</mn></msub><mi>n1</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A2n2</mi><mo>=</mo><msub><msub><mi>A</mi><mn>2</mn></msub><mi>n2</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am1n3</mi><mo>=</mo><msub><msub><mi>A</mi><mi>m1</mi></msub><mi>n3</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am2n4</mi><mo>=</mo><msub><msub><mi>A</mi><mi>m2</mi></msub><mi>n4</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am3n5</mi><mo>=</mo><msub><msub><mi>A</mi><mi>m3</mi></msub><mi>n5</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am4n6</mi><mo>=</mo><msub><msub><mi>A</mi><mi>m4</mi></msub><mi>n6</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am5n7</mi><mo>=</mo><msub><msub><mi>A</mi><mi>m5</mi></msub><mi>n7</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am6n8</mi><mo>=</mo><msub><msub><mi>A</mi><mi>m6</mi></msub><mi>n8</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd><mtd><mfrac><mn>10</mn><mn>3</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mfrac><mn>9</mn><mn>5</mn></mfrac></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mfrac><mn>10</mn><mn>3</mn></mfrac></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>7</mn><mn>3</mn></mfrac></mtd><mtd><mn>2</mn></mtd><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>7</mn></mtd><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mn>9</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mfrac><mn>8</mn><mn>5</mn></mfrac></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mfrac><mn>8</mn><mn>5</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd><mtd><mo>-</mo><mn>10</mn></mtd><mtd><mn>7</mn></mtd><mtd><mo>-</mo><mn>8</mn></mtd><mtd><mo>-</mo><mfrac><mn>6</mn><mn>5</mn></mfrac></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am1n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am2n4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Am3n5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A2n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Propiedades y Matrices Especiales/Tipos de Matrices Tipos de matrices: antisimétrica #enunciado 1.0000000 0.1000000 0 0 #a <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>Escribe</mi><mo> </mo><mi>una</mi><mo> </mo><mi>matriz</mi><mo> </mo><mi>antisimétrica</mi><mo> </mo><mo>(</mo><mi>o</mi><mo> </mo><mi>hemisimétrica</mi><mo>)</mo><mo> </mo><mi>de</mi><mo> </mo><mi>orden</mi><mo> </mo><mn>3</mn><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>=</mo><mo>-</mo><msup><mi>x</mi><mo>T</mo></msup><mo>∧</mo><mi>longitud</mi><mo>(</mo><mi>columna</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>=</mo><mn>3</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mo>T</mo></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>longitud</mi><mo>(</mo><mi>columna</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>=</mo><mn>3</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><msup><mi>a</mi><mo>T</mo></msup><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Tipos de matrices: escalonada #enunciado 1.0000000 0.1000000 0 0 #a <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>Escribe</mi><mo> </mo><mi>una</mi><mo> </mo><mi>matriz</mi><mo> </mo><mi>escalonada</mi><mo> </mo><mi>de</mi><mo> </mo><mi>dimensiones</mi><mo> </mo><mn>3</mn><mi>x2</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><msub><mi>x</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><mi>n_filas</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>∧</mo><mi>n_columnas</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_filas</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_columnas</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Tipos de matrices: identidad #enunciado 1.0000000 0.1000000 0 0 #sol <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>q</mi><mo>=</mo><mo>&quot;</mo><mi>identidad</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>q</mi><mo>=</mo><mo>&quot;</mo><mi>unidad</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><ident definitionURL="http://www.wiris.com/XML/csymbol"/><mi>u</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>Escribe</mi><mo> </mo><mi>la</mi><mo> </mo><mi>matriz</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mi>de</mi><mo> </mo><mi>orden</mi><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>q</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>unidad</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Escribe</ms><mo> </mo><ms>la</ms><mo> </mo><ms>matriz</ms><mo> </mo><ms>unidad</ms><mo> </mo><ms>de</ms><mo> </mo><ms>orden</ms><mo> </mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Tipos de matrices: nula #enunciado 1.0000000 0.1000000 0 0 #a <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>Escribe</mi><mo> </mo><mi>una</mi><mo> </mo><mi>matriz</mi><mo> </mo><mi>nula</mi><mo> </mo><mi>de</mi><mo> </mo><mi>dimensiones</mi><mo> </mo><mn>2</mn><mi>x3</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><msub><mi>x</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><mi>n_filas</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>∧</mo><mi>n_columnas</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_filas</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_columnas</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Tipos de matrices: simétrica #enunciado 1.0000000 0.1000000 0 0 #a <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>Escribe</mi><mo> </mo><mi>una</mi><mo> </mo><mi>matriz</mi><mo> </mo><mi>simétrica</mi><mo> </mo><mi>de</mi><mo> </mo><mi>orden</mi><mo> </mo><mn>3</mn><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>=</mo><msup><mi>x</mi><mo>T</mo></msup><mo>∧</mo><mi>longitud</mi><mo>(</mo><mi>columna</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>=</mo><mn>3</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mo>T</mo></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>longitud</mi><mo>(</mo><mi>columna</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>=</mo><mn>3</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Tipos de matrices: traspuesta Dada la matriz A = #A, escribe la matriz traspuesta de A 1.0000000 0.1000000 0 0 #B <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><msup><mi>A</mi><mo>T</mo></msup></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><msup><mi>A</mi><mo>T</mo></msup></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><msup><mi>A</mi><mo>T</mo></msup></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><msup><mi>A</mi><mo>T</mo></msup></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>Dada</mi><mo> </mo><mi>la</mi><mo> </mo><mi>matriz</mi><mo> </mo><mi>A</mi><mo>=</mo><mo>#</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>escribe</mi><mo> </mo><mi>la</mi><mo> </mo><mi>matriz</mi><mo> </mo><mi>traspuesta</mi><mo> </mo><mi>de</mi><mo> </mo><mi>A</mi><mo>&quot;</mo><mo>,</mo><mi>A</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Dada</ms><mo> </mo><ms>la</ms><mo> </mo><ms>matriz</ms><mo> </mo><ms>A</ms><mo>=</mo><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable></mfenced><ms>,</ms><mo> </mo><ms>escribe</ms><mo> </mo><ms>la</ms><mo> </mo><ms>matriz</ms><mo> </mo><ms>traspuesta</ms><mo> </mo><ms>de</ms><mo> </mo><ms>A</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#B</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Tipos de matrices: triangular superior #enunciado 1.0000000 0.1000000 0 0 #a <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>Escribe</mi><mo> </mo><mi>una</mi><mo> </mo><mi>matriz</mi><mo> </mo><mi>triangular</mi><mo> </mo><mi>superior</mi><mo> </mo><mi>de</mi><mo> </mo><mi>orden</mi><mo> </mo><mn>3</mn><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><msub><mi>x</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><msub><mi>x</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>∧</mo><mi>n_filas</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>∧</mo><mi>n_columnas</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>≠</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>b</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_filas</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_columnas</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>b</mi><mo>)</mo></math></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Sistemas de Ecuaciones 02 - Forma Matricial de un SEL «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#LS1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#LS2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#LS3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

cuales son las matrices asociados a dicho sistema, de la forma «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»·«/mo»«mi»x«/mi»«mo»=«/mo»«mi»b«/mi»«/math»?

]]> 1.0000000 0.1000000 0 0 A=#Ab=#b ]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>a2</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>a3</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>b2</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>b3</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>c2</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>c3</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>s</mi><mo>:</mo><mo>=</mo></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></mtd></mtr></mtable></mfenced><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mn>0</mn></mtd></mtr></mtable></mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn></mtd></mtr></mtable></mfenced></apply></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c1</mi><mo>·</mo><mi>z</mi><mo>=</mo><msub><mi>s</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c2</mi><mo>·</mo><mi>z</mi><mo>=</mo><msub><mi>s</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS3</mi><mo>=</mo><mi>a3</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b3</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c3</mi><mo>·</mo><mi>z</mi><mo>=</mo><msub><mi>s</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a1</mi></mtd><mtd><mi>b1</mi></mtd><mtd><mi>c1</mi></mtd></mtr><mtr><mtd><mi>a2</mi></mtd><mtd><mi>b2</mi></mtd><mtd><mi>c2</mi></mtd></mtr><mtr><mtd><mi>a3</mi></mtd><mtd><mi>b3</mi></mtd><mtd><mi>c3</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msup><mfenced close="]" open="["><mrow><msub><mi>s</mi><mn>1</mn></msub><mo>,</mo><msub><mi>s</mi><mn>2</mn></msub><mo>,</mo><msub><mi>s</mi><mn>3</mn></msub></mrow></mfenced><mo>T</mo></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>7</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo>#</mo><mi>A</mi><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo>#</mo><mi>b</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 03 - Identificar un Sistema Homogeneo
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#LS1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#LS2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#LS3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»
]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>a2</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>a3</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>b2</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>b3</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>c2</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>c3</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ks</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>s</mi><mo>:</mo><mo>=</mo></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ks</mi><mo>=</mo><mn>1</mn></mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn></mtd></mtr></mtable></mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></apply></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kr</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r</mi><mo>:</mo><mo>=</mo></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>kr</mi><mo>=</mo><mn>1</mn></mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn></mtd></mtr></mtable></mfenced><mrow><mi>kr</mi><mo>=</mo><mn>2</mn></mrow><mi>s</mi><mrow><mi>kr</mi><mo>=</mo><mn>3</mn></mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></apply></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c1</mi><mo>·</mo><mi>z</mi><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><mo>=</mo><msub><mi>s</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c2</mi><mo>·</mo><mi>z</mi><mo>+</mo><msub><mi>r</mi><mn>2</mn></msub><mo>=</mo><msub><mi>s</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS3</mi><mo>=</mo><mi>a3</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b3</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c3</mi><mo>·</mo><mi>z</mi><mo>+</mo><msub><mi>r</mi><mn>3</mn></msub><mo>=</mo><msub><mi>s</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mfenced><mrow><mi>r</mi><mo>=</mo><mi>s</mi><mo> </mo><mo>?</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>-</mo><mn>6</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>z</mi><mo>-</mo><mn>8</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>false</mi></math></output></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 04 - Resolver sistema 3x3 Clasifique el siguiente sistema

#a·x+#b·y+#c·z=#j

#d·x+#e·y+#f·z=#k

#g·x+#h·y+#i·z=#l

]]> 1.0000000 0.1000000 0 true true abc #buena #mala #mala1 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mtr</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mtr2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>j</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd><mtd><mi>k</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd><mtd><mi>l</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>rango</mi><mo>(</mo><mi>mtr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>rango</mi><mo>(</mo><mi>mtr2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mo>&quot;</mo><mi>Sistema</mi><mo> </mo><mi>compatible</mi><mo> </mo><mi>determinado</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mo>&quot;</mo><mi>Sistema</mi><mo> </mo><mi>compatible</mi><mo> </mo><mi>indeterminado</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mo>&quot;</mo><mi>Sistema</mi><mo> </mo><mi>incompatible</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r</mi><mo>=</mo><mi>r2</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>r</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>buena</mi><mo>=</mo><mi>aa</mi></mtd></mtr><mtr><mtd><mi>mala</mi><mo>=</mo><mi>bb</mi></mtd></mtr><mtr><mtd><mi>mala1</mi><mo>=</mo><mi>cc</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r</mi><mo>&lt;</mo><mi>r2</mi></mrow><mtable><mtr><mtd><mi>buena</mi><mo>=</mo><mi>cc</mi></mtd></mtr><mtr><mtd><mi>mala</mi><mo>=</mo><mi>bb</mi></mtd></mtr><mtr><mtd><mi>mala1</mi><mo>=</mo><mi>aa</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>buena</mi><mo>=</mo><mi>bb</mi></mtd></mtr><mtr><mtd><mi>mala</mi><mo>=</mo><mi>cc</mi></mtd></mtr><mtr><mtd><mi>mala1</mi><mo>=</mo><mi>aa</mi></mtd></mtr></mtable></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>buena</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Sistema</ms><mo> </mo><ms>incompatible</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mala</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Sistema</ms><mo> </mo><ms>compatible</ms><mo> </mo><ms>indeterminado</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mala1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Sistema</ms><mo> </mo><ms>compatible</ms><mo> </mo><ms>determinado</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> 07 - Sistema de Ecuaciones 3x3 consistente determinado
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mrow»«mtable»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c1«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b2«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c2«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a3«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b3«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c3«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d3«/mi»«/mtd»«/mtr»«/mtable»«mo»§nbsp;«/mo»«/mrow»«/mfenced»«/math»

NOTA: Si se trata de un sistema compatible indeterminado, considera z como variable libre escribiendo z = k y escribe la x y la y en función de k (recuerda anotar la multiplicación entre coeficiente y parte literal con un ·)
]]> 1.0000000 0.1000000 0 0 x=#xy=#yz=#z]]> Muy bien. Se trata de un sistema compatible determinado y estaes su única solución. <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>list</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mi>L</mi></mrow><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>b</mi><mo>,</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>a</mi><mn>1</mn></msub></mtd><mtd><msub><mi>b</mi><mn>1</mn></msub></mtd><mtd><msub><mi>c</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mn>2</mn></msub></mtd><mtd><msub><mi>b</mi><mn>2</mn></msub></mtd><mtd><msub><mi>c</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mn>3</mn></msub></mtd><mtd><msub><mi>b</mi><mn>3</mn></msub></mtd><mtd><msub><mi>c</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mi>A</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mi>L</mi></mrow><mrow><mi>d</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>d</mi><mo>,</mo><msub><mi>a</mi><mi>i</mi></msub><mo>·</mo><mi>x</mi><mo>+</mo><msub><mi>b</mi><mi>i</mi></msub><mo>·</mo><mi>y</mi><mo>+</mo><msub><mi>c</mi><mi>i</mi></msub><mo>·</mo><mi>z</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msub><mi>a</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msub><mi>a</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><msub><mi>a</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><mi>b</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><mi>b</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><msub><mi>b</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>c</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msub><mi>c</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><msub><mi>c</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msub><mi>d</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><msub><mi>d</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><msub><mi>d</mi><mn>3</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>29</mn><mo>,</mo><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mn>21</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>z</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> 08 - Sistema de 3x3 con infinitas soluciones
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨¨ close=¨}¨»«mrow»«mtable»«mtr»«mtd»«mi»#a11«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»#a12«/mi»«mo»§#183;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»#a13«/mi»«mo»§#183;«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a21«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»#a22«/mi»«mo»§#183;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»#a23«/mi»«mo»§#183;«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a31«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»#a32«/mi»«mo»§#183;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»#a33«/mi»«mo»§#183;«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d3«/mi»«/mtd»«/mtr»«/mtable»«mo»§#160;«/mo»«/mrow»«/mfenced»«/math»

NOTA: Si se trata de un sistema compatible indeterminado, considera z como variable libre escribiendo z = k y escribe la «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» y la «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«/math» en función de k (recuerda anotar la multiplicación entre coeficiente y parte literal con un ·)
]]> 1.0000000 0.1000000 0 0 x=#r1y=#s1z=#t1]]> Muy bien. Se trata de un sistema compatible indeterminado y tiene infinitas soluciones. <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>constant_matrix</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>constant_matrix</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Li</mi><mo>=</mo><mi>list</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lj</mi><mo>=</mo><mi>list</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mi>Li</mi></mrow><mtable><mtr><mtd><msub><mi>b</mi><mi>i</mi></msub><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>j</mi><mo> </mo><mi>in</mi><mo> </mo><mi>Lj</mi></mrow><mrow><msub><mi>A</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mrow></apply></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>A</mi><mn>3</mn></msub><mo>=</mo><mi>a</mi><mo>·</mo><msub><mi>A</mi><mn>1</mn></msub><mo>+</mo><msub><mi>A</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>b</mi><mn>3</mn></msub><mo>=</mo><mi>a</mi><mo>·</mo><msub><mi>b</mi><mn>1</mn></msub><mo>+</mo><msub><mi>b</mi><mn>2</mn></msub></mtd></mtr></mtable><mrow><mi>rank</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mo>=</mo><mi>rank</mi><mo>(</mo><mi>A</mi><mo>|</mo><mi>b</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>k</mi><mo>·</mo><msub><mi>T</mi><mn>1</mn></msub><mo>+</mo><msup><msub><mi>T</mi><mn>2</mn></msub><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a21</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a31</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a22</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a32</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a13</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a23</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a33</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msub><mi>b</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><msub><mi>b</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><msub><mi>b</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x</mi><mo>=</mo><mi>r1</mi></mrow><mrow><mi>return</mi><mo> </mo><mi>true</mi></mrow><mrow><mi>return</mi><mo> </mo><mi>false</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x</mi><mo>=</mo><mi>s1</mi></mrow><mrow><mi>return</mi><mo> </mo><mi>true</mi></mrow><mrow><mi>return</mi><mo> </mo><mi>false</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x</mi><mo>=</mo><mi>t1</mi></mrow><mrow><mi>return</mi><mo> </mo><mi>true</mi></mrow><mrow><mi>return</mi><mo> </mo><mi>false</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>T</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>5</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>18</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>10</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>8</mn></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced><mtable><mtr><mtd><mo>-</mo><mfrac><mn>5</mn><mn>7</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>4</mn><mn>7</mn></mfrac></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>,</mo><mfrac><mn>22</mn><mn>7</mn></mfrac><mo>,</mo><mn>0</mn></mrow></mfenced></mtd></mtr></mtable></mfenced><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>8</mn></mrow></mfenced><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>s</mi><mn>1</mn><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>t</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">r #s #t</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> 09 - Resolución Sistema 2x2
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»-«/mo»«mi»#b2«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c2«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.1000000 0 0 x=#xy=#y]]> Muy bien. <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mfrac><mi>a2</mi><mi>a1</mi></mfrac><mo>==</mo><mfrac><mrow><mo>-</mo><mi>b2</mi></mrow><mi>b1</mi></mfrac></mrow><mtable><mtr><mtd><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>·</mo><mi>y</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>#x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mi>#y</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Sistemas de Ecuaciones/Sistemas de 2x2 y otros 01 - Identificar sistema de 2x2 en el grafico Asociar los siguientes graficos con sus nombres correctos]]> 1.0000000 0.1000000 0 true #p11 Sistema incompatible #p22 Sistema compatible determinado #p3 Sistema compatible indeterminado <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>·</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>·</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>·</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>a</mi><mo>≠</mo><mi>c</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>·</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>b</mi><mo>≠</mo><mi>d</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>t1</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>=</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>}</mo><mo>,</mo><mi>x</mi><mo>,</mo><mo>-</mo><mn>12</mn><mo>.</mo><mo>.</mo><mn>12</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>p1</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>=</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>}</mo><mo>,</mo><mi>x</mi><mo>,</mo><mo>-</mo><mn>12</mn><mo>.</mo><mo>.</mo><mn>12</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>t2</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>=</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>}</mo><mo>,</mo><mi>x</mi><mo>,</mo><mo>-</mo><mn>12</mn><mo>.</mo><mo>.</mo><mn>12</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p22</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>p2</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>=</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>}</mo><mo>,</mo><mi>x</mi><mo>,</mo><mo>-</mo><mn>12</mn><mo>.</mo><mo>.</mo><mn>12</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>t3</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>=</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>}</mo><mo>,</mo><mi>x</mi><mo>,</mo><mo>-</mo><mn>12</mn><mo>.</mo><mo>.</mo><mn>12</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> 05 - Problema de planteo 2x2 Hallar la velocidad, en metros por segundo, de 2 automóviles sabiendo que se mueven, partiendo en el mismo instante y del mismo lugar, alrededor de una pista circular de 1km de longitud, y que cuando se mueven en direcciones opuestas se cruzan cada #a segundos, mientras que cuando lo hacen en la misma dirección se cruzan cada #b segundos.

¿Velocidad del coche A? (velocidad mayor)

{#1}

¿Velocidad del coche B? (velocidad menor)

{#2}

Nota: Expresarlos en forma de fracción.

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>85</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vb</mi><mo>=</mo><mfrac><mrow><mn>1000</mn><mo>*</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>a</mi><mo>)</mo></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mfrac><mrow><mn>1000</mn><mo>-</mo><mi>a</mi><mo>*</mo><mi>vb</mi></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>91</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10600</mn><mn>273</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7600</mn><mn>273</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> CS ALG SIST resolución sistema dos ecuaciones
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»-«/mo»«mi»#b2«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c2«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

NOTACIÓN de la respuesta:

x=
y=

]]> 1.0000000 0.1000000 0 0 x=#xy=#y]]> Muy bien. <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>·</mo><mi>y</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>#x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mi>#y</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">x #y</param></assertion></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> CS ALG SIST resolución sistema dos ecuaciones 2
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»=«/mo»«mi»#c1«/mi»«mo»-«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#aux1«/mi»«/mrow»«mi»#aux2«/mi»«/mfrac»«mo»=«/mo»«mi»#c22«/mi»«mo»+«/mo»«mi»#b22«/mi»«mo»·«/mo»«mi»y«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

NOTACIÓN de la respuesta:

x=
y=

]]> 1.0000000 0.1000000 0 0 x=#xy=#y]]> Muy bien. <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mfrac><mi>a2</mi><mi>a1</mi></mfrac><mo>==</mo><mfrac><mrow><mo>-</mo><mi>b2</mi></mrow><mi>b1</mi></mfrac></mrow><mtable><mtr><mtd><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c22</mi><mo>=</mo><mfrac><mrow><mi>c2</mi><mo>+</mo><mi>aux1</mi></mrow><mi>aux2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b22</mi><mo>=</mo><mfrac><mi>b2</mi><mi>aux2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>#x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mi>#y</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> CS ALG SIST resolución sistema dos ecuaciones 2
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»=«/mo»«mi»#c1«/mi»«mo»-«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#aux1«/mi»«/mrow»«mi»#aux2«/mi»«/mfrac»«mo»=«/mo»«mi»#c22«/mi»«mo»+«/mo»«mi»#b22«/mi»«mo»·«/mo»«mi»y«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

NOTACIÓN de la respuesta:

x=
y=

]]> 1.0000000 0.1000000 0 0 x=#xy=#y]]> Muy bien. <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c22</mi><mo>=</mo><mfrac><mrow><mi>c2</mi><mo>+</mo><mi>aux1</mi></mrow><mi>aux2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b22</mi><mo>=</mo><mfrac><mi>b2</mi><mi>aux2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>#x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mi>#y</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">x #y</param></assertion></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> CS ALG SIST resolución sistema dos ecuaciones 3
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#c22«/mi»«mo»+«/mo»«mi»#b22«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#aux1«/mi»«/mrow»«mi»#aux2«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»=«/mo»«mi»#c1«/mi»«mo»-«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

NOTACIÓN de la respuesta:

x=
y=

]]> 1.0000000 0.1000000 0 0 x=#xy=#y]]> Muy bien. <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c22</mi><mo>=</mo><mfrac><mrow><mi>c2</mi><mo>+</mo><mi>aux1</mi></mrow><mi>aux2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b22</mi><mo>=</mo><mfrac><mi>b2</mi><mi>aux2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>#x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mi>#y</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">x #y</param></assertion></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> CS ALG SIST resolución sistema dos ecuaciones 3
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#c22«/mi»«mo»+«/mo»«mi»#b22«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#aux1«/mi»«/mrow»«mi»#aux2«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»=«/mo»«mi»#c1«/mi»«mo»-«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

NOTACIÓN de la respuesta:

x=
y=

]]> 1.0000000 0.1000000 0 0 x=#xy=#y]]> Muy bien. <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mfrac><mi>a2</mi><mi>a1</mi></mfrac><mo>==</mo><mfrac><mrow><mo>-</mo><mi>b2</mi></mrow><mi>b1</mi></mfrac></mrow><mtable><mtr><mtd><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>b2</mi><mo>·</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c22</mi><mo>=</mo><mfrac><mrow><mi>c2</mi><mo>+</mo><mi>aux1</mi></mrow><mi>aux2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b22</mi><mo>=</mo><mfrac><mi>b2</mi><mi>aux2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>#x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mi>#y</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> Resolución de un sistema de ecuaciones de 2x2 por el método de Gauss-Jordan

#ecu1 = #e

#ecu2 = #f

Utiliza el método de Gauss-Jordan para resolver el sistema de ecuaciones realizando las operaciones sugeridas:

	#a	#b	#e
	#c	#d	#f
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mo»(«/mo»«mi»#c«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»-«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#a«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»	{#1}	{#2}	{#3}
	{#4}	{#5}	{#6}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mfrac»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mrow»«mi»#q«/mi»«/mrow»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»	{#7}	{#8}	{#9}
	{#10}	{#11}	{#12}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#b«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»	{#13}	{#14}	{#15}
	{#16}	{#17}	{#18}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mrow»«mi»#a«/mi»«/mrow»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/math»	{#19}	{#20}	{#21}
	{#22}	{#23}	{#24}

]]> 24.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mtd></mtr></mtable><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>∧</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>b</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>c</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>d</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>q</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>e</mi></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a2</mi><mo>=</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>e</mi></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a3</mi><mo>=</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>c3</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e3</mi><mo>=</mo><mi>e</mi><mo>-</mo><mi>b</mi><mo>*</mo><mo>(</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>f3</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a4</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>c4</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e4</mi><mo>=</mo><mfrac><mrow><mi>e</mi><mo>-</mo><mi>b</mi><mo>*</mo><mo>(</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac><mo>)</mo></mrow><mi>a</mi></mfrac></mtd></mtr><mtr><mtd><mi>f4</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command></group></library></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Resolución de un sistema de ecuaciones de 2x2 por el método de Gauss-Jordan 2

#ecu1 = #e

#ecu2 = #f

Utiliza el método de Gauss-Jordan para resolver el sistema de ecuaciones con las operaciones planteadas:

	#a	#b	#e
	#c	#d	#f
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mo»(«/mo»«mi»#c«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»-«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#a«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»	{#1}	{#2}	{#3}
	{#4}	{#5}	{#6}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo largeop=¨true¨»§#8764;«/mo»«mrow»«mfrac»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mrow»«mi»#q«/mi»«/mrow»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/munder»«/math»	{#7}	{#8}	{#9}
	{#10}	{#11}	{#12}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8764;«/mo»«mrow»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»-«/mo»«mo»(«/mo»«mi»#b«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/munder»«/math»	{#13}	{#14}	{#15}
	{#16}	{#17}	{#18}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mrow»«mi»#a«/mi»«/mrow»«/mfrac»«mo»§#8594;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/math»	{#19}	{#20}	{#21}
	{#22}	{#23}	{#24}

]]> 24.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>∧</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>b</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>c</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>d</mi><mo>≠</mo><mn>1</mn><mo>∧</mo><mi>q</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>e</mi></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a2</mi><mo>=</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>e</mi></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a3</mi><mo>=</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>c3</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e3</mi><mo>=</mo><mi>e</mi><mo>-</mo><mi>b</mi><mo>*</mo><mo>(</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>f3</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a4</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>c4</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e4</mi><mo>=</mo><mfrac><mrow><mi>e</mi><mo>-</mo><mi>b</mi><mo>*</mo><mo>(</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac><mo>)</mo></mrow><mi>a</mi></mfrac></mtd></mtr><mtr><mtd><mi>f4</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>e</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi></mrow><mrow><mi>b</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>d</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command></group></library></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Sistema de ecuaciones 3x3 Método de Cramer

#ecu1 = #b1

#ecu2 = #b2

#ecu3 = #b3

Utiliza el método de Cramer para encontrar la solución al sistema de ecuaciones anteriores.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mrow»«mi»s«/mi»«mo»=«/mo»«/mrow»«/msub»«/math»{#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mrow»«mi»x«/mi»«mo»=«/mo»«/mrow»«/msub»«/math»={#2}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mi»y«/mi»«/msub»«mo»=«/mo»«/math»{#3}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mi»z«/mi»«/msub»«mo»=«/mo»«/math»{#4}

Por lo tanto:

x={#5}/ {#6}

={#7}

y={#8}/ {#9}

={#10}

z={#11}/ {#12}

={#13}

]]> 13.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>c</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>d</mi><mo>(</mo><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>n</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dime</mi><mo>=</mo><mi>dimensiones</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>j</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi></mrow><mrow><msub><msub><mi>A</mi><mi>i</mi></msub><mi>j</mi></msub><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><msub><msub><mi>B</mi><mi>i</mi></msub><mn>1</mn></msub><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></apply><mrow><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>DetX</mi><mo>=</mo><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetX</mi><mn>1</mn></msub><mn>1</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>1</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetX</mi><mn>2</mn></msub><mn>1</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>2</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetX</mi><mn>3</mn></msub><mn>1</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>3</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>DetY</mi><mo>=</mo><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetY</mi><mn>1</mn></msub><mn>2</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>1</mn></msub><mn>1</mn></msub></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><mi>B</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><msub><mi>B</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>9</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>6</mn><mn>5</mn></mfrac></mtd><mtd><mn>9</mn></mtd><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1627</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Sistema de ecuaciones 4x4 método de Cramer

#ecu1 = #b1

#ecu2 = #b2

#ecu3 = #b3

#ecu4 = #b4

Utiliza el método de Cramer para encontrar la solución al sistema de ecuaciones anteriores.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mrow»«mi»s«/mi»«mo»=«/mo»«/mrow»«/msub»«/math»{#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mrow»«mi»w«/mi»«mo»=«/mo»«/mrow»«/msub»«/math»={#2}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mrow»«mi»x«/mi»«mo»=«/mo»«/mrow»«/msub»«/math»={#3}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mi»y«/mi»«/msub»«mo»=«/mo»«/math»{#4}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#916;«/mi»«mi»z«/mi»«/msub»«mo»=«/mo»«/math»{#5}

Por lo tanto:

w={#6}/ {#7}

={#8}

x={#9}/ {#10}

={#11}

y={#12}/ {#13}

={#14}

z={#15}/ {#16}

={#17}

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu2</mi><mo>=</mo><msub><msub><mi>A</mi><mn>2</mn></msub><mn>1</mn></msub><mo>*</mo><mi>w</mi><mo>+</mo><msub><msub><mi>A</mi><mn>2</mn></msub><mn>2</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><msub><mi>A</mi><mn>2</mn></msub><mn>3</mn></msub><mo>*</mo><mi>y</mi><mo>+</mo><msub><msub><mi>A</mi><mn>2</mn></msub><mn>4</mn></msub><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu3</mi><mo>=</mo><msub><msub><mi>A</mi><mn>3</mn></msub><mn>1</mn></msub><mo>*</mo><mi>w</mi><mo>+</mo><msub><msub><mi>A</mi><mn>3</mn></msub><mn>2</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><msub><mi>A</mi><mn>3</mn></msub><mn>3</mn></msub><mo>*</mo><mi>y</mi><mo>+</mo><msub><msub><mi>A</mi><mn>3</mn></msub><mn>4</mn></msub><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu4</mi><mo>=</mo><msub><msub><mi>A</mi><mn>4</mn></msub><mn>1</mn></msub><mo>*</mo><mi>w</mi><mo>+</mo><msub><msub><mi>A</mi><mn>4</mn></msub><mn>2</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><msub><mi>A</mi><mn>4</mn></msub><mn>3</mn></msub><mo>*</mo><mi>y</mi><mo>+</mo><msub><msub><mi>A</mi><mn>4</mn></msub><mn>4</mn></msub><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><msub><mi>B</mi><mn>1</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><msub><mi>B</mi><mn>2</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><msub><msub><mi>B</mi><mn>3</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>=</mo><msub><msub><mi>B</mi><mn>4</mn></msub><mn>1</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mfrac><mn>7</mn><mn>2</mn></mfrac></mtd><mtd><mo>-</mo><mn>8</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mfrac><mn>2</mn><mn>5</mn></mfrac></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mo>-</mo><mfrac><mn>7</mn><mn>3</mn></mfrac></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mfrac><mn>9</mn><mn>2</mn></mfrac></mtd><mtd><mo>-</mo><mn>7</mn></mtd><mtd><mfrac><mn>2</mn><mn>5</mn></mfrac></mtd><mtd><mo>-</mo><mn>7</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>26413</mn><mn>50</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> ÁLGEBRA 2/2. ESPACIOS VECTORIALES 01- Dependencia Lineal La siguiente afirmación: "Los vectores «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»,«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»g«/mi»«mo»,«/mo»«mo»#«/mo»«mi»h«/mi»«mo»,«/mo»«mo»#«/mo»«mi»i«/mi»«mo»)«/mo»«mo»§#160;«/mo»«/math»son linealmente dependiente es"

]]>
Sean «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mover»«msub»«mi»v«/mi»«mn»1«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mn»2«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mn»3«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mi»n«/mi»«/msub»«mo»§#8640;«/mo»«/mover»«/mrow»«/mfenced»«/math» un conjunto de vectores de una espacio V y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#945;«/mi»«mn»1«/mn»«/msub»«mo»,«/mo»«msub»«mi»§#945;«/mi»«mn»2«/mn»«/msub»«mo»,«/mo»«msub»«mi»§#945;«/mi»«mn»3«/mn»«/msub»«mo»,«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»,«/mo»«msub»«mi»§#945;«/mi»«mi»n«/mi»«/msub»«/math» escalares (numeros reales) entonces, si al resolver la ecuación

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#945;«/mi»«mn»1«/mn»«/msub»«mo»§#183;«/mo»«mover»«msub»«mi»v«/mi»«mn»1«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«msub»«mi»§#945;«/mi»«mn»2«/mn»«/msub»«mo»§#183;«/mo»«mover»«msub»«mi»v«/mi»«mn»2«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«msub»«mi»§#945;«/mi»«mn»3«/mn»«/msub»«mo»§#183;«/mo»«mover»«msub»«mi»v«/mi»«mn»3«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»+«/mo»«msub»«mi»§#945;«/mi»«mi»n«/mi»«/msub»«mo»§#183;«/mo»«mover»«msub»«mi»v«/mi»«mi»n«/mi»«/msub»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mn»0«/mn»«/math»

nos da que todos los escalares («math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#945;«/mi»«mn»1«/mn»«/msub»«mo»,«/mo»«msub»«mi»§#945;«/mi»«mn»2«/mn»«/msub»«mo»,«/mo»«msub»«mi»§#945;«/mi»«mn»3«/mn»«/msub»«mo»,«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»,«/mo»«msub»«mi»§#945;«/mi»«mi»n«/mi»«/msub»«/math») son cero entonces los vectores «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mover»«msub»«mi»v«/mi»«mn»1«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mn»2«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mn»3«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mi»n«/mi»«/msub»«mo»§#8640;«/mo»«/mover»«/mrow»«/mfenced»«/math» son linealmente independientes (l.i.) si al resolver dicha ecuación tenemos por lo menos una solución distinta a la que todos deben ser cero (por ejemplo, puede ser infinitas soluciones) serán los vectores «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mover»«msub»«mi»v«/mi»«mn»1«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mn»2«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mn»3«/mn»«/msub»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»,«/mo»«mover»«msub»«mi»v«/mi»«mi»n«/mi»«/msub»«mo»§#8640;«/mo»«/mover»«/mrow»«/mfenced»«/math» linealmente dependientes (l.d.)

obs. En la ecuación el 0 es el vector cero del espacio V (puede ser la matriz cero, el polinomio cero, etc. dependiendo del conjunto donde trabajemos).

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced close="|" open="|"><mi>A</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mfenced close="|" open="|"><mi>A</mi></mfenced><mo>=</mo><mn>0</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 02 - Dependencia Lineal polinomios La siguiente afirmación: "Los vectores «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»{«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»3«/mn»«mo»}«/mo»«/math» son linealmente dependiente es"

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol2</mi><mo>=</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol3</mi><mo>=</mo><mi>g</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>h</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced close="|" open="|"><mi>A</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mfenced close="|" open="|"><mi>A</mi></mfenced><mo>=</mo><mn>0</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>38</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 03 - Base de R3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math»?

{#1}

]]> Como la dimensión de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math» es 3, necesitamos tres vectores linealmente independientes para que sean base. Por lo que, sólo debemos probar que los tres vectores dados sean l.i.

{#1}

]]> Como la dimensión de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»4«/mn»«/msup»«/math» es 4, debemos tener 4 vectores linealmente independientes de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»4«/mn»«/msup»«/math». Sólo debemos ver que los vectores dados sean l.i.

]]> 1.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mtrz</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr><mtr><mtd><mi>i</mi></mtd><mtd><mi>j</mi></mtd><mtd><mi>k</mi></mtd><mtd><mi>l</mi></mtd></mtr><mtr><mtd><mi>m</mi></mtd><mtd><mi>q</mi></mtd><mtd><mi>p</mi></mtd><mtd><mi>o</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mo>"</mo><mi>Sí</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mo>"</mo><mi>No</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>rango</mi><mo>(</mo><mi>mtrz</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r</mi><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>mala</mi><mo>=</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>buena</mi><mo>=</mo><mi>s</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>mala</mi><mo>=</mo><mi>s</mi></mtd></mtr><mtr><mtd><mi>buena</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mtrz</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>buena</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>No</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 04 - Combinación lineal «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math», determinar los escalares que forman al vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»i«/mi»«mo»^«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mn»1«/mn»«mo»,«/mo»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«mo»)«/mo»«/math», respecto de la base dada. (obs. respete el orden en que se entrega la base)

({#1},{#2},{#3})

]]> 3.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>K</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>d</mi></mtd><mtd><mi>g</mi></mtd></mtr><mtr><mtd><mi>b</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>h</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>f</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced></mrow><mrow><mfenced close="&verbar;" open="&verbar;"><mi>K</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>u</mi></mtd></mtr><mtr><mtd><mi>v</mi></mtd></mtr><mtr><mtd><mi>w</mi></mtd></mtr></mtable></mfenced><mo>=</mo><msup><mi>K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mfrac><mn>4</mn><mn>11</mn></mfrac></mtd><mtd><mfrac><mn>7</mn><mn>11</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>2</mn><mn>11</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>3</mn><mn>11</mn></mfrac></mtd><mtd><mfrac><mn>3</mn><mn>11</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>4</mn><mn>11</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>3</mn><mn>11</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>8</mn><mn>11</mn></mfrac></mtd><mtd><mfrac><mn>7</mn><mn>11</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>11</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>11</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>11</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> 04 - Pertenece al subespacio generado (matrices) La afimración "La Matrices #M1 pertenece al subespacio generado por el conjunto { #M2, #M3 }" es

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>i</mi></mtd><mtd><mi>j</mi></mtd></mtr><mtr><mtd><mi>k</mi></mtd><mtd><mi>l</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp1</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>linealmente_independientes</mi><mo>?</mo><mo>(</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>,</mo><mo>[</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>]</mo><mo>,</mo><mo>[</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>]</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resp1</mi><mo>=</mo><mi>cierto</mi></mrow><mrow><mi>sol</mi><mo>:</mo><mo>=</mo><mi>falso</mi></mrow><mrow><mi>sol</mi><mo>:</mo><mo>=</mo><mi>cierto</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 06 - L.I. o L.D. Matrices (copia) La afirmación "Las Matrices #M1, #M2 y #M3 son lineamente Independientes es"

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>i</mi></mtd><mtd><mi>j</mi></mtd></mtr><mtr><mtd><mi>k</mi></mtd><mtd><mi>l</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>linealmente_independientes</mi><mo>?</mo><mo>(</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>,</mo><mo>[</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>]</mo><mo>,</mo><mo>[</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>]</mo><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ÁLGEBRA 2/2. ESPACIOS VECTORIALES/Combinacion Lineal 04 - Comibacion lineal de R3 ?

{#1}

]]> Debemos recordar que un vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«/math» es combinación lineal de otros vectores, por ejemplo, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#160;«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mover»«mi»w«/mi»«mo»§#8640;«/mo»«/mover»«/math» si existen escalares (numeros reales) que permitan escribirlo de la forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mi»§#945;«/mi»«mo»§#183;«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«mi»§#946;«/mi»«mo»§#183;«/mo»«mover»«mi»w«/mi»«mo»§#8640;«/mo»«/mover»«/math»

si esta última ecuación tiene solución diremos que el vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«/math» es combinación lineal de los vectores «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mover»«mi»w«/mi»«mo»§#8640;«/mo»«/mover»«/math». De lo contrario diremos que no es combinación lineal.

En este ejercicio debes resolver la ecuación:

Si el sistema formado tiene solución, entonces, es combinación lineal. De lo contrario no es combinación lineal.

]]> Para que una matriz sea combinación lineal de otras (en este caso de #M2 y #M3) debe ocurrir que existen escalares «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»§#946;«/mi»«/math» tales que se cumple:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»M«/mi»«mn»1«/mn»«mo»=«/mo»«mi»§#945;«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»M«/mi»«mn»2«/mn»«mo»+«/mo»«mi»§#946;«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»M«/mi»«mn»3«/mn»«/math»

Si el sistema que se forma anterior no tiene solución, se dice que #M1 NO es combinación lineal de #M2 y #M3.

Si el sistema que se forma tiene solución, se dice que #M1 es combinación lineal de #M2 y #M3

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>i</mi></mtd><mtd><mi>j</mi></mtd></mtr><mtr><mtd><mi>k</mi></mtd><mtd><mi>l</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>linealmente_independientes</mi><mo>?</mo><mo>(</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>,</mo><mo>[</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>]</mo><mo>,</mo><mo>[</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>]</mo><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>falso</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Combinacion lineal (pregunta inicial)

Determinar los valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»§#946;«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mi»§#948;«/mi»«/math» para que el vector (#a,#b,#c) sea combinación lineal de (#d,#e,#f), (#g,#h,#i) y (#j, #k , #l)

obs: respete el orden en el cual fue entregado los vectores y utilice valores exactos para ingresar sus respuesta (no decimales)

]]> Para que el vector (#a,#b,#c) sea combinación lineal de (#d,#e,#f), (#g,#h,#i) y (#j,#k,#l) se debe escribir de la forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»=«/mo»«mi»§#945;«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»+«/mo»«mi»§#946;«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»g«/mi»«mo»,«/mo»«mo»#«/mo»«mi»h«/mi»«mo»,«/mo»«mo»#«/mo»«mi»i«/mi»«mo»)«/mo»«mo»+«/mo»«mi»§#948;«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»j«/mi»«mo»,«/mo»«mo»#«/mo»«mi»k«/mi»«mo»,«/mo»«mo»#«/mo»«mi»l«/mi»«mo»)«/mo»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»§#945;«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#183;«/mo»«mi»§#945;«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»§#183;«/mo»«mi»§#945;«/mi»«mo»)«/mo»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»§#946;«/mi»«mo»,«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#183;«/mo»«mi»§#946;«/mi»«mo»,«/mo»«mo»#«/mo»«mi»i«/mi»«mo»§#183;«/mo»«mi»§#946;«/mi»«mo»)«/mo»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»j«/mi»«mo»§#183;«/mo»«mi»§#948;«/mi»«mo»,«/mo»«mo»#«/mo»«mi»k«/mi»«mo»§#183;«/mo»«mi»§#948;«/mi»«mo»,«/mo»«mo»#«/mo»«mi»l«/mi»«mo»§#183;«/mo»«mi»§#948;«/mi»«mo»)«/mo»«/math»

Esto nos lleva a resolver el sistema:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«menclose notation=¨right¨»«menclose notation=¨bottom¨»«mo»#«/mo»«mi»a«/mi»«mo»=«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»§#945;«/mi»«mo»+«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»§#946;«/mi»«mo»+«/mo»«mo»#«/mo»«mi»j«/mi»«mo»§#183;«/mo»«mi»§#948;«/mi»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»b«/mi»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#183;«/mo»«mi»§#945;«/mi»«mo»+«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#183;«/mo»«mi»§#946;«/mi»«mo»+«/mo»«mo»#«/mo»«mi»k«/mi»«mo»§#183;«/mo»«mi»§#948;«/mi»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»c«/mi»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mo»§#183;«/mo»«mi»§#945;«/mi»«mo»+«/mo»«mo»#«/mo»«mi»i«/mi»«mo»§#183;«/mo»«mi»§#946;«/mi»«mo»+«/mo»«mo»#«/mo»«mi»l«/mi»«mo»§#183;«/mo»«mi»§#948;«/mi»«/menclose»«/menclose»«/math»

Finalmente podemos comprobar que se cumple:

(#a, #b, #c)=#Sol1 (#d,#e,#f)+#Sol2 (#g,#h,#i)+#Sol3 (#j,#k,#l)

]]> 1.0000000 0.3333333 0 0 α=#Sol1β=#Sol2δ=#Sol3]]> ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr><mtr><mtd><mi>j</mi></mtd><mtd><mi>k</mi></mtd><mtd><mi>l</mi></mtd></mtr></mtable></mfenced></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>=</mo><mi>x</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>y</mi><mo>*</mo><mi>g</mi><mo>+</mo><mi>z</mi><mo>*</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>x</mi><mo>*</mo><mi>e</mi><mo>+</mo><mi>y</mi><mo>*</mo><mi>h</mi><mo>+</mo><mi>z</mi><mo>*</mo><mi>k</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>x</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>y</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>z</mi><mo>*</mo><mi>l</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol2</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol3</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mo>#</mo><mi>S</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>β</mi><mo>=</mo><mo>#</mo><mi>S</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>δ</mi><mo>=</mo><mo>#</mo><mi>S</mi><mi>o</mi><mi>l</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">33 33 34</data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Combinacion lineal (pregunta inicial) (polinomio)

Determinar los valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»§#946;«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mi»§#948;«/mi»«/math» para que el vector #pol1 sea combinación lineal de #pol2 ; #pol3 ; #pol4

obs: respete el orden en el cual fue entregado los vectores

]]> Para que #pol1 sea combinación lineal de #pol2; #pol3 y #pol4 , deben existir escalares «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»§#946;«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mi»§#948;«/mi»«/math» tales que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»=«/mo»«mi»§#945;«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«mo»)«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»§#946;«/mi»«mo»§#183;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»3«/mn»«mo»)«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»§#948;«/mi»«mo»§#183;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»4«/mn»«mo»)«/mo»«/math»

distribuimos

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»3«/mn»«/math»

agrupamos

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»)«/mo»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»)«/mo»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»3«/mn»«mo»)«/mo»«/math»

igualando coeficientes (dos polinomios son iguales si sus coeficientes son iguales)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«menclose notation=¨right¨»«menclose notation=¨bottom¨»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»b«/mi»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»c«/mi»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»3«/mn»«/menclose»«/menclose»«/math»

Resolviendo este sistema tenemos los valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»=«/mo»«mo»#«/mo»«mi»S«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»§#946;«/mi»«mo»=«/mo»«mo»#«/mo»«mi»S«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»§#948;«/mi»«mo»=«/mo»«mo»#«/mo»«mi»S«/mi»«mi»o«/mi»«mi»l«/mi»«mn»3«/mn»«/math»

ademas podemos comprobar que

#pol1=#Sol1 (#pol2)+#Sol2 (#pol3)+#Sol3 (#pol4)

]]> 1.0000000 0.3333333 0 0 α=#Sol1β=#Sol2δ=#Sol3]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr><mtr><mtd><mi>j</mi></mtd><mtd><mi>k</mi></mtd><mtd><mi>l</mi></mtd></mtr></mtable></mfenced></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol2</mi><mo>=</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol3</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>β</mi><mo>*</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>β</mi><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>β</mi><mo>*</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>δ</mi><mo>*</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>δ</mi><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>δ</mi><mo>*</mo><mi>l</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>b1</mi><mo>+</mo><mi>c1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>b2</mi><mo>+</mo><mi>c2</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>α</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mo>#</mo><mi>S</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>β</mi><mo>=</mo><mo>#</mo><mi>S</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>δ</mi><mo>=</mo><mo>#</mo><mi>S</mi><mi>o</mi><mi>l</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">33 33 34</data><data name="casSession"/><data name="inputCompound">true</data></localData></question> ÁLGEBRA 2/2. ESPACIOS VECTORIALES/control 6 02 - Dimensión espacio generado y representación geometrica Cual es la dimensión del subespacio formado por ellos: (ingrese sólo el numero)

{#1}

]]> 1.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mtrz</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>rango</mi><mo>(</mo><mi>mtrz</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>&quot;</mo><mi>Recta</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mo>&quot;</mo><mi>Plano</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>&quot;</mo><mi>Espacio</mi><mo> </mo><mi>completo</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>mala1</mi><mo>=</mo><mi>p</mi></mtd></mtr><mtr><mtd><mi>mala2</mi><mo>=</mo><mi>t</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>p</mi></mtd></mtr><mtr><mtd><mi>mala1</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>mala2</mi><mo>=</mo><mi>t</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>t</mi></mtd></mtr><mtr><mtd><mi>mala1</mi><mo>=</mo><mi>p</mi></mtd></mtr><mtr><mtd><mi>mala2</mi><mo>=</mo><mi>r</mi></mtd></mtr></mtable></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> 05 - Pertenece al subespacio generado (R3) La afirmación

"El vector (#a, #b, #c) pertenece al subespacio generado por { (#d, #e, #f), (#g, #h, #i) }"

es:

]]> 1.0000000 1.0000000 0 Verdadero Falso Recuerda que: "para que un vector pertenezca al espacio generado, debe ser combinación lineal del conjunto generador."

{#1}

]]>

Recuerde que un subespacio debe cumplir tres condiciones:

1) El vector cero debe pertenecer a T

2) Si tenemos dos vectores cualesquiera de T, por ejemplo: u y v su suma debe seguir siendo un elemento de T

3) Sea k un numero real, y \( \vec{u} \) un vector cualquiera de T, la multiplicación de \( k \cdot \vec{u} \) debe ser un elemento de T

Si el conjunto dado, no cumple una de estas condiciones, no puede ser un subespacio vectorial.

{#1}

]]> Recuerde que un subespacio debe cumplir tres condiciones:

1) El vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mn»0«/mn»«mo»§#8640;«/mo»«/mover»«/math» debe pertenecer a T

2) Si tenemos dos vectores cualesquiera de T, por ejemplo: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«/math» su suma debe seguir siendo un elemento de T

3) Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«/math» un numero real, y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«/math» un vector cualquiera de T, la multiplicación de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»§#183;«/mo»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«/math» debe ser un elemento de T

Si el conjunto dado, no cumple una de estas condiciones, no puede ser un subespacio vectorial.

{#1}

]]> Recuerde que un subespacio debe cumplir tres condiciones:

1) El vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mn»0«/mn»«mo»§#8640;«/mo»«/mover»«/math» (en este caso la matriz 0) debe pertenecer a T

2) Si tenemos dos vectores (en este caso son matrices) cualesquiera de T, por ejemplo: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«/math», su suma debe seguir siendo un elemento de T (es decir luego de sumar se debe obtener siempre una matriz que siga cumpliendo las condicion de T)

3) Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«/math» un numero real, y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«/math» un vector (en este caso matriz) cualquiera de T, la multiplicación de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»§#183;«/mo»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«/math» debe ser un elemento de T (es decir luego de multiplicar se debe obtener siempre una matriz que siga cumpliendo las condicion de T)

Si el conjunto dado, no cumple una de estas condiciones, no puede ser un subespacio vectorial.

{#1}

]]> Recuerde que un subespacio debe cumplir tres condiciones:

1) El vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mn»0«/mn»«mo»§#8640;«/mo»«/mover»«/math» (en este caso la matriz 0) debe pertenecer a T

3) Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«/math» un numero real, y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«/math» un vector (en este caso matriz) cualquiera de T, la multiplicación de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»§#183;«/mo»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«/math» debe ser un elemento de T (es decir luego de multiplicar se debe obtener siempre una matriz que siga cumpliendo las condicion de T)

Si el conjunto dado, no cumple una de estas condiciones, no puede ser un subespacio vectorial.

({#1},{#2},{#3})

]]> 3.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>K</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>d</mi></mtd><mtd><mi>g</mi></mtd></mtr><mtr><mtd><mi>b</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>h</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>f</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced></mrow><mrow><mfenced close="|" open="|"><mi>K</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>u</mi></mtd></mtr><mtr><mtd><mi>v</mi></mtd></mtr><mtr><mtd><mi>w</mi></mtd></mtr></mtable></mfenced><mo>=</mo><msup><mi>K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><mfenced><mtable><mtr><mtd><mi>j</mi></mtd></mtr><mtr><mtd><mi>k</mi></mtd></mtr><mtr><mtd><mi>l</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 03 - Determinar T(x,y,z) de una transformación

({#1},{#2})

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>t3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mi>v1</mi></mtd><mtd><mi>v2</mi></mtd><mtd><mi>v3</mi></mtd></mtr><mtr><mtd><mi>w1</mi></mtd><mtd><mi>w2</mi></mtd><mtd><mi>w3</mi></mtd></mtr><mtr><mtd><mi>t1</mi></mtd><mtd><mi>t2</mi></mtd><mtd><mi>t3</mi></mtd></mtr></mtable></mfenced></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>v1</mi><mo>+</mo><mi>β</mi><mo>*</mo><mi>w1</mi><mo>+</mo><mi>γ</mi><mo>*</mo><mi>t1</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>v2</mi><mo>+</mo><mi>β</mi><mo>*</mo><mi>w2</mi><mo>+</mo><mi>γ</mi><mo>*</mo><mi>t2</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>v3</mi><mo>+</mo><mi>β</mi><mo>*</mo><mi>w3</mi><mo>+</mo><mi>γ</mi><mo>*</mo><mi>t3</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mo>{</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>c</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>b</mi><mo>≠</mo><mi>d</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>e</mi><mo>≠</mo><mi>c</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo><mo>*</mo><mi>a</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo><mo>*</mo><mi>c</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>γ</mi><mo>)</mo><mo>*</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo><mo>*</mo><mi>b</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo><mo>*</mo><mi>d</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>γ</mi><mo>)</mo><mo>*</mo><mi>f</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>γ</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>y</mi><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>z</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 06 - Determinar T(x,y), (base no canonica)

({#1},{#2})

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>t3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mi>v1</mi></mtd><mtd><mi>v2</mi></mtd><mtd><mi>v3</mi></mtd></mtr><mtr><mtd><mi>w1</mi></mtd><mtd><mi>w2</mi></mtd><mtd><mi>w3</mi></mtd></mtr><mtr><mtd><mi>t1</mi></mtd><mtd><mi>t2</mi></mtd><mtd><mi>t3</mi></mtd></mtr></mtable></mfenced></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>v1</mi><mo>+</mo><mi>β</mi><mo>*</mo><mi>w1</mi><mo>+</mo><mi>γ</mi><mo>*</mo><mi>t1</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>v2</mi><mo>+</mo><mi>β</mi><mo>*</mo><mi>w2</mi><mo>+</mo><mi>γ</mi><mo>*</mo><mi>t2</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>v3</mi><mo>+</mo><mi>β</mi><mo>*</mo><mi>w3</mi><mo>+</mo><mi>γ</mi><mo>*</mo><mi>t3</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mo>{</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>g</mi><mo>≠</mo><mi>i</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>h</mi><mo>≠</mo><mi>d</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>e</mi><mo>≠</mo><mi>c</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>v1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>v3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol2</mi><mo>=</mo><mi>w1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>w2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>w3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol3</mi><mo>=</mo><mi>t1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>t2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>t3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo><mo>*</mo><mi>g</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo><mo>*</mo><mi>i</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>γ</mi><mo>)</mo><mo>*</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo><mo>*</mo><mi>h</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo><mo>*</mo><mi>d</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>γ</mi><mo>)</mo><mo>*</mo><mi>f</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>-</mo><mi>c</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>γ</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>-</mo><mi>b</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 07 - Matriz de transformación (bases canonicas) Determinar la matriz de transformación respecto de la base canonica de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»:«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«mo»§#8594;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math» donde «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»,«/mo»«mi»z«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»3«/mn»«mo»)«/mo»«/math»

({#1},{#2})

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>w2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>w3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mi>v2</mi></mtd><mtd><mi>v3</mi></mtd></mtr><mtr><mtd><mi>w2</mi></mtd><mtd><mi>w3</mi></mtd></mtr></mtable></mfenced></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>v2</mi><mo>+</mo><mi>β</mi><mo>*</mo><mi>w2</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>α</mi><mo>*</mo><mi>v3</mi><mo>+</mo><mi>β</mi><mo>*</mo><mi>w3</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mo>{</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>g</mi><mo>≠</mo><mi>i</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>h</mi><mo>≠</mo><mi>d</mi><mo> </mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>v3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol2</mi><mo>=</mo><mi>w2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>w3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo><mo>*</mo><mi>g</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo><mo>*</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo><mo>*</mo><mi>h</mi><mo>+</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo><mo>*</mo><mi>d</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>α</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>11</mn></mfrac><mo>*</mo><mi>a</mi><mo>+</mo><mfrac><mn>3</mn><mn>22</mn></mfrac><mo>*</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>β</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>11</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mfrac><mn>2</mn><mn>11</mn></mfrac><mo>*</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 08 - Matriz de transformación (bases canonicas R2 a R3) Determinar la matriz de transformación respecto de la base canonica de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»:«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«mo»§#8594;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math» donde «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»3«/mn»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mi>b1</mi></mtd><mtd><mi>b2</mi></mtd></mtr><mtr><mtd><mi>c1</mi></mtd><mtd><mi>c2</mi></mtd></mtr></mtable></mfenced></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp1</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>b1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>b2</mi><mo>}</mo><mo>)</mo></mtd><mtd><mi>evaluar</mi><mo>(</mo><mi>exp1</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>c1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>c2</mi><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp2</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>b1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>b2</mi><mo>}</mo><mo>)</mo></mtd><mtd><mi>evaluar</mi><mo>(</mo><mi>exp2</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>c1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>c2</mi><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp3</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>b1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>b2</mi><mo>}</mo><mo>)</mo></mtd><mtd><mi>evaluar</mi><mo>(</mo><mi>exp3</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>c1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>c2</mi><mo>}</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>10</mn></mtd></mtr><mtr><mtd><mn>21</mn></mtd><mtd><mo>-</mo><mn>7</mn></mtd></mtr><mtr><mtd><mn>10</mn></mtd><mtd><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 10 - Matriz de transformación (bases no canonicas R2 a R3) Determinar la matriz de transformación respecto de la base «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»)«/mo»«mo»,«/mo»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»)«/mo»«/mrow»«/mfenced»«/math» de«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«/math» y la base «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»d«/mi»«mn»3«/mn»«mo»)«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mn»3«/mn»«mo»)«/mo»«mo»,«/mo»«mo»(«/mo»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»f«/mi»«mn»3«/mn»«mo»)«/mo»«/mrow»«/mfenced»«/math» de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math», donde se define «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»:«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«mo»§#8594;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math» con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»3«/mn»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mi>b1</mi></mtd><mtd><mi>b2</mi></mtd></mtr><mtr><mtd><mi>c1</mi></mtd><mtd><mi>c2</mi></mtd></mtr></mtable></mfenced></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mi>d1</mi></mtd><mtd><mi>d2</mi></mtd><mtd><mi>d3</mi></mtd></mtr><mtr><mtd><mi>e1</mi></mtd><mtd><mi>e2</mi></mtd><mtd><mi>e3</mi></mtd></mtr><mtr><mtd><mi>f1</mi></mtd><mtd><mi>f2</mi></mtd><mtd><mi>f3</mi></mtd></mtr></mtable></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp1</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>b1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>b2</mi><mo>}</mo><mo>)</mo><mo>=</mo><mi>x1</mi><mo>*</mo><mi>d1</mi><mo>+</mo><mi>y1</mi><mo>*</mo><mi>e1</mi><mo>+</mo><mi>z1</mi><mo>*</mo><mi>f1</mi></mtd></mtr><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp2</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>b1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>b2</mi><mo>}</mo><mo>)</mo><mo>=</mo><mi>x1</mi><mo>*</mo><mi>d2</mi><mo>+</mo><mi>y1</mi><mo>*</mo><mi>e2</mi><mo>+</mo><mi>z1</mi><mo>*</mo><mi>f2</mi></mtd></mtr><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp3</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>b1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>b2</mi><mo>}</mo><mo>)</mo><mo>=</mo><mi>x1</mi><mo>*</mo><mi>d3</mi><mo>+</mo><mi>y1</mi><mo>*</mo><mi>e3</mi><mo>+</mo><mi>z1</mi><mo>*</mo><mi>f3</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp1</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>c1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>c2</mi><mo>}</mo><mo>)</mo><mo>=</mo><mi>x1</mi><mo>*</mo><mi>d1</mi><mo>+</mo><mi>y1</mi><mo>*</mo><mi>e1</mi><mo>+</mo><mi>z1</mi><mo>*</mo><mi>f1</mi></mtd></mtr><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp2</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>c1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>c2</mi><mo>}</mo><mo>)</mo><mo>=</mo><mi>x1</mi><mo>*</mo><mi>d2</mi><mo>+</mo><mi>y1</mi><mo>*</mo><mi>e2</mi><mo>+</mo><mi>z1</mi><mo>*</mo><mi>f2</mi></mtd></mtr><mtr><mtd><mi>evaluar</mi><mo>(</mo><mi>exp3</mi><mo>,</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>c1</mi><mo>,</mo><mi>y</mi><mo>→</mo><mi>c2</mi><mo>}</mo><mo>)</mo><mo>=</mo><mi>x1</mi><mo>*</mo><mi>d3</mi><mo>+</mo><mi>y1</mi><mo>*</mo><mi>e3</mi><mo>+</mo><mi>z1</mi><mo>*</mo><mi>f3</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x1</mi><mo>)</mo></mtd><mtd><msub><mi>T</mi><mn>1</mn></msub><mo>(</mo><mi>x1</mi><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>y1</mi><mo>)</mo></mtd><mtd><msub><mi>T</mi><mn>1</mn></msub><mo>(</mo><mi>y1</mi><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>z1</mi><mo>)</mo></mtd><mtd><msub><mi>T</mi><mn>1</mn></msub><mo>(</mo><mi>z1</mi><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mfrac><mn>3</mn><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>23</mn><mn>4</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>21</mn><mn>8</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>11</mn><mn>2</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>17</mn><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ÁLGEBRA 2/3. APLICACIONES LINEALES/Def Transformacion Lineal 00- Definición de transf lineal

{#1}

]]> i) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«/math» debe preservar la suma es decir, para todo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»,«/mo»«mo»§#160;«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«/math»; «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»)«/mo»«mo»=«/mo»«mi»T«/mi»«mo»(«/mo»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»)«/mo»«mo»+«/mo»«mi»T«/mi»«mo»(«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»)«/mo»«/math»
ii) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«/math» debe preservar el producto escalar, es decir, para todo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#955;«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» entonces; «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mi»§#955;«/mi»«mo»§#183;«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»)«/mo»«mo»=«/mo»«mi»§#955;«/mi»«mo»§#183;«/mo»«mi»T«/mi»«mo»(«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»)«/mo»«/math»

Si cumple estas dos propiedades podemos decir que T es aplicación lineal (o transformación lineal)
]]> 1.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>,</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>,</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mi>x</mi><mo>,</mo><mn>2</mn><mi>y</mi><mo>+</mo><mi>c</mi><mo>,</mo><mn>2</mn><mi>x</mi><mo>+</mo><mi>c</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp3</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>,</mo><mi>y</mi><mo>-</mo><mi>x</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>buena</mi><mo>=</mo><mi>NO</mi></mtd></mtr><mtr><mtd><mi>mala</mi><mo>=</mo><mi>SI</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>buena</mi><mo>=</mo><mi>SI</mi></mtd></mtr><mtr><mtd><mi>mala</mi><mo>=</mo><mi>NO</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>buena</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SI</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 02 - Imagen de un vector (propiedades)

({#1},{#2})

]]> 1.0000000 0.3333333 0 0 x1=#sol1y1=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>c</mi><mo>≠</mo><mi>d</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>e</mi><mo>≠</mo><mi>f</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>y</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 04 - Imagen de un polinomio a un vector R2 Calcular las coordenadas «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»,«/mo»«mo»§#160;«/mo»«msub»«mi»y«/mi»«mn»1«/mn»«/msub»«mo»)«/mo»«/math» del vector imagen, del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«/math» al ingresar en la aplicacion lineal «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»:«/mo»«msub»«mi»P«/mi»«mn»2«/mn»«/msub»«mo»(«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»)«/mo»«mo»§#8594;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«/math» definida por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mi»a«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»2«/mn»«mo»)«/mo»«/math»

obs: El conjunto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»P«/mi»«mn»2«/mn»«/msub»«mo»(«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»)«/mo»«/math», se refiere al espacio vectorial de los polinomios de grado a lo mas dos.

]]> 1.0000000 0.3333333 0 0 x1=#sol1y1=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>,</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>,</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>,</mo><mo>-</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo>,</mo><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>exp1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mrow><mi>sol1</mi><mo>=</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>+</mo><mi>f</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>exp1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>sol1</mi><mo>=</mo><mi>d</mi><mo>+</mo><mi>e</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>exp1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>c</mi></mrow><mrow><mi>sol1</mi><mo>=</mo><mi>d</mi><mo>+</mo><mi>f</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>exp2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>-</mo><mi>c</mi></mrow><mrow><mi>sol2</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>e</mi><mo>-</mo><mi>f</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>exp2</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>-</mo><mi>c</mi></mrow><mrow><mi>sol2</mi><mo>=</mo><mo>-</mo><mi>d</mi><mo>-</mo><mi>f</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>exp2</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>sol2</mi><mo>=</mo><mo>-</mo><mi>d</mi><mo>-</mo><mi>e</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>y</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 05 - Imagen de un par odenado a un polinomio Determine la imagen del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»v«/mi»«mi»a«/mi»«mi»l«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»v«/mi»«mi»a«/mi»«mi»l«/mi»«mn»2«/mn»«mo»)«/mo»«/math» en la aplicación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»:«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«mo»§#8594;«/mo»«msub»«mi»P«/mi»«mn»2«/mn»«/msub»«mo»(«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»)«/mo»«/math», definida por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»1«/mn»«mo»)«/mo»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»2«/mn»«mo»)«/mo»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»3«/mn»«/math». Entonces «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mo»#«/mo»«mi»v«/mi»«mi»a«/mi»«mi»l«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»v«/mi»«mi»a«/mi»«mi»l«/mi»«mn»2«/mn»«mo»)«/mo»«/math»=

]]> 1.0000000 0.3333333 0 0 #sol1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>val1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>val2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>val1</mi><mo>≠</mo><mi>val2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi><mo>=</mo><mi>d</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>e</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp3</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><mi>exp1</mi><mo>,</mo><mo>{</mo><mi>a</mi><mo>→</mo><mi>val1</mi><mo>,</mo><mi>b</mi><mo>→</mo><mi>val2</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><mi>exp2</mi><mo>,</mo><mo>{</mo><mi>a</mi><mo>→</mo><mi>val1</mi><mo>,</mo><mi>b</mi><mo>→</mo><mi>val2</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><mi>exp3</mi><mo>,</mo><mo>{</mo><mi>a</mi><mo>→</mo><mi>val1</mi><mo>,</mo><mi>b</mi><mo>→</mo><mi>val2</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>val1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>val2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>12</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 06 - Imagen de una matriz a R3 Determinar las coordenadas (x₁, y₁, z₁) de la imagen de #M1 al ingresar a la aplicación lineal «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»:«/mo»«msub»«mi»M«/mi»«mn»2«/mn»«/msub»«mo»(«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»)«/mo»«mo»§#8594;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math», definida por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»c«/mi»«/mtd»«mtd»«mi»d«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»3«/mn»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 x1=#sol1y1=#sol2z1=#sol3]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>j</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi><mo>=</mo><mi>j</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>i</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp3</mi><mo>=</mo><mi>k</mi><mo>*</mo><mi>a</mi><mo>-</mo><mi>j</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><mi>exp1</mi><mo>,</mo><mo>{</mo><mi>a</mi><mo>→</mo><mi>e</mi><mo>,</mo><mi>b</mi><mo>→</mo><mi>f</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><mi>exp2</mi><mo>,</mo><mo>{</mo><mi>c</mi><mo>→</mo><mi>g</mi><mo>,</mo><mi>d</mi><mo>→</mo><mi>h</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><mi>exp3</mi><mo>,</mo><mo>{</mo><mi>a</mi><mo>→</mo><mi>e</mi><mo>,</mo><mi>c</mi><mo>→</mo><mi>g</mi><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>y</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><msub><mi>z</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ÁLGEBRA 2/3. APLICACIONES LINEALES/Def. Núcleo 00 - Pertenece al núcleo R2 en R2 Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»:«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«mo»§#8594;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«/math» una aplicación lineal definida por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mfenced»«mrow»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»2«/mn»«mo»)«/mo»«/math» , Indique un vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»)«/mo»«/math» , distinto del vector cero, que pertenezca al núcleo de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«/math»

]]> Primero debemos recordar la definición de núcleo de una transformación linea, el conjunto núcleo de una transformación, son todos los vectores que tienen por imagen el vector cero del espacio de llegada.

Entonces, debe indicar un vector que nos de por imagen el «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«mo»)«/mo»«/math» (esto porque es una función de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«mo»§#8594;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«/math»), es decir buscamos un (a,b) tal que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«mo»)«/mo»«/math» como tiene infinitas respuestas el sistema no entregará una solución especifica, si tiene dudas puede acercarse a su profesor.

]]> 1.0000000 0.3333333 0 0 a=#ab=#b]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable><mrow><mi>c</mi><mo>*</mo><mi>f</mi><mo>-</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp2</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>y</mi><mo>*</mo><mi>d</mi><mo>=</mo><mn>0</mn><mo> </mo><mo>∧</mo><mo> </mo><mi>x</mi><mo>*</mo><mi>e</mi><mo>+</mo><mi>y</mi><mo>*</mo><mi>f</mi><mo>=</mo><mn>0</mn><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>x</mi><mo>≠</mo><mn>0</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>y</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo>#</mo><mi>b</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 01 - Pertenece al núcleo Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»:«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«mo»§#8594;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» una aplicación lineal definida por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mfenced»«mrow»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mn»1«/mn»«/math» , Indique un vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»)«/mo»«/math» , distinto del vector cero, que pertenezca al núcleo de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«/math»

]]> Debe indicar un vector que nos de por imagen el 0 (esto porque es una función de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«mo»§#8594;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»), es decir buscamos un (a,b) tal que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»(«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»)«/mo»«mo»=«/mo»«mn»0«/mn»«/math» como tiene infinitas respuestas solamente daremos un ejemplo de respuesta.

]]> 1.0000000 0.3333333 0 0 a=#ab=#b]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>c</mi><mo>/</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>y</mi><mo>*</mo><mi>d</mi><mo>=</mo><mn>0</mn><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>x</mi><mo>≠</mo><mn>0</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>y</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>exp1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo>#</mo><mi>b</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> ÁLGEBRA 2/3. APLICACIONES LINEALES/Diagonalización 01 - Polinomio caracteristico Determine el polinomio caracteristico de la matriz #m1

obs: El polinomio debe ser escrito con la variable x.

]]> Recuerde que el polinomio caracteristico se obtiene se define como «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»|«/mo»«mi»A«/mi»«mo»-«/mo»«mi»x«/mi»«mo»§#183;«/mo»«msub»«mi»I«/mi»«mi»n«/mi»«/msub»«mo»|«/mo»«/math», donde «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mi»n«/mi»«/msub»«/math» es la matriz identidad de tamaño igual al tamaño de la matriz A

obs: El polinomio debe ser escrito con la variable x, no es necesario factorizar.

]]> 1.0000000 0.3333333 0 0 #sol1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>a</mi></mtd><mtd><mi>h</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mo>-</mo><mi>polinomio_caracteristico</mi><mo>(</mo><mi>m1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>polinomio_caracteristico</mi><mo>(</mo><mi>m1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>=</mo><mi>sol1</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>x</mi><mo>=</mo><mi>sol2</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 01 - valores propios Determinar los valores propios de #m1

obs: Ingrese su respuesta de menor a mayor

]]> Recuerde que son los valores propios son las raices del polinomio caracteristico, es decir, primero debemos encontrar el polinomio caracteristico, este es:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»§#955;«/mi»«mo»)«/mo»«mo»=«/mo»«mi»d«/mi»«mi»e«/mi»«mi»t«/mi»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»§#955;«/mi»«mo»§#183;«/mo»«mi»I«/mi»«mo»)«/mo»«mo»=«/mo»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mi»§#955;«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»c«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»d«/mi»«mo»-«/mo»«mi»§#955;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«/math»

Por lo que las raices de dicho polinomio son #Sol1 y #Sol2

]]> 1.0000000 0.3333333 0 0 λ1=#Sol1λ2=#Sol2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></mtd></mtr></mtable><mrow><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>+</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></msqrt><mo>∈</mo><integers/><mo> </mo><mo>∧</mo><mo> </mo><mi>a</mi><mo>≠</mo><mi>b</mi><mo>≠</mo><mi>d</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>valores_propios</mi><mo>(</mo><mi>m1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol2</mi><mo>=</mo><msub><mi>S</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>polinomio_caracteristico</mi><mo>(</mo><mi>m1</mi><mo>,</mo><mi>λ</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>12</mn></mtd><mtd><mn>15</mn></mtd></mtr><mtr><mtd><mn>19</mn></mtd><mtd><mn>8</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>7</mn><mo>,</mo><mn>27</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>λ</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>λ</mi><mo>-</mo><mn>189</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mn>1</mn><mo>=</mo><mo>#</mo><mi>S</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>λ</mi><mn>2</mn><mo>=</mo><mo>#</mo><mi>S</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question>