ÁLGEBRA 2/3. APLICACIONES LINEALES 01 - Coordenadas de un vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math», determinar las coordenadas del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»i«/mi»«mo»^«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»j«/mi»«mo»,«/mo»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«mo»)«/mo»«/math», respecto de la base dada.

({#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>