ÁLGEBRA 2/1. MATRICES y SISTEMAS DE ECUACIONES/Sistemas de Ecuaciones 02 - Forma Matricial de un SEL «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#LS1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#LS2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#LS3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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

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

#a·x+#b·y+#c·z=#j

#d·x+#e·y+#f·z=#k

#g·x+#h·y+#i·z=#l

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

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

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

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

¿Velocidad del coche A? (velocidad mayor)

{#1}

¿Velocidad del coche B? (velocidad menor)

{#2}

Nota: Expresarlos en forma de fracción.

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

NOTACIÓN de la respuesta:

x=
y=

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

NOTACIÓN de la respuesta:

x=
y=

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

NOTACIÓN de la respuesta:

x=
y=

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

NOTACIÓN de la respuesta:

x=
y=

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

NOTACIÓN de la respuesta:

x=
y=

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

#ecu1 = #e

#ecu2 = #f

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

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

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

#ecu1 = #e

#ecu2 = #f

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

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

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

#ecu1 = #b1

#ecu2 = #b2

#ecu3 = #b3

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

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

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

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

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

Por lo tanto:

x={#5}/ {#6}

={#7}

y={#8}/ {#9}

={#10}

z={#11}/ {#12}

={#13}

]]> 13.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>c</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>d</mi><mo>(</mo><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>n</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dime</mi><mo>=</mo><mi>dimensiones</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>j</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi></mrow><mrow><msub><msub><mi>A</mi><mi>i</mi></msub><mi>j</mi></msub><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><msub><msub><mi>B</mi><mi>i</mi></msub><mn>1</mn></msub><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></apply><mrow><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>DetX</mi><mo>=</mo><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetX</mi><mn>1</mn></msub><mn>1</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>1</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetX</mi><mn>2</mn></msub><mn>1</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>2</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetX</mi><mn>3</mn></msub><mn>1</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>3</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>DetY</mi><mo>=</mo><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetY</mi><mn>1</mn></msub><mn>2</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>1</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetY</mi><mn>2</mn></msub><mn>2</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>2</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetY</mi><mn>3</mn></msub><mn>2</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>3</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>DetZ</mi><mo>=</mo><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetZ</mi><mn>1</mn></msub><mn>3</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>1</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetZ</mi><mn>2</mn></msub><mn>3</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>2</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><msub><mi>DetZ</mi><mn>3</mn></msub><mn>3</mn></msub><mo>=</mo><msub><msub><mi>B</mi><mn>3</mn></msub><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>deltax</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>DetX</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>deltay</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>DetY</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>deltaz</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>DetZ</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>deltax</mi><mo>/</mo><mi>de</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>deltay</mi><mo>/</mo><mi>de</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>zs</mi><mo>=</mo><mi>deltaz</mi><mo>/</mo><mi>de</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu1</mi><mo>=</mo><msub><msub><mi>A</mi><mn>1</mn></msub><mn>1</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><msub><mi>A</mi><mn>1</mn></msub><mn>2</mn></msub><mo>*</mo><mi>y</mi><mo>+</mo><msub><msub><mi>A</mi><mn>1</mn></msub><mn>3</mn></msub><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu2</mi><mo>=</mo><msub><msub><mi>A</mi><mn>2</mn></msub><mn>1</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><msub><mi>A</mi><mn>2</mn></msub><mn>2</mn></msub><mo>*</mo><mi>y</mi><mo>+</mo><msub><msub><mi>A</mi><mn>2</mn></msub><mn>3</mn></msub><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu3</mi><mo>=</mo><msub><msub><mi>A</mi><mn>3</mn></msub><mn>1</mn></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><msub><mi>A</mi><mn>3</mn></msub><mn>2</mn></msub><mo>*</mo><mi>y</mi><mo>+</mo><msub><msub><mi>A</mi><mn>3</mn></msub><mn>3</mn></msub><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><mi>B</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><mi>B</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><msub><mi>B</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>9</mn></mtd><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>6</mn><mn>5</mn></mfrac></mtd><mtd><mn>9</mn></mtd><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>9</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1627</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Sistema de ecuaciones 4x4 método de Cramer

#ecu1 = #b1

#ecu2 = #b2

#ecu3 = #b3

#ecu4 = #b4

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

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

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

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

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

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

Por lo tanto:

w={#6}/ {#7}

={#8}

x={#9}/ {#10}

={#11}

y={#12}/ {#13}

={#14}

z={#15}/ {#16}

={#17}

]]> 17.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>c</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>d</mi><mo>(</mo><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>n</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dime</mi><mo>=</mo><mi>dimensiones</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>j</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi></mrow><mrow><msub><msub><mi>A</mi><mi>i</mi></msub><mi>j</mi></msub><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><msub><msub><mi>B</mi><mi>i</mi></msub><mn>1</mn></msub><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></apply><mrow><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>DetW</mi><mo>=</mo><mi>A</mi></math></input></command><command><input><math 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