Cálculo/Control 3/Medio C3 - CII - Determinante 4 - M Pregunta: C3 - CII - Determinante 4 - M

Dada la matriz

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»#«/mo»«mi»A«/mi»«/math»

Determine los valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#955;«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» , tal que el determinante de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«/math» sea cero.

OBS: Escriba la solución como conjunto de la siguiente forma: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»{«/mo»«mo»{«/mo»«mi»§#955;«/mi»«mo»=«/mo»«mi»a«/mi»«mo»}«/mo»«mo»,«/mo»«mo»{«/mo»«mi»§#955;«/mi»«mo»=«/mo»«mi»b«/mi»«mo»}«/mo»«mo»,«/mo»«mo»{«/mo»«mi»§#955;«/mi»«mo»=«/mo»«mi»c«/mi»«mo»}«/mo»«mo»}«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn><mo>-</mo><mi>λ</mi></mtd><mtd><mn>2</mn></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>a</mi><mo>-</mo><mi>λ</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>d</mi></mtd><mtd><mi>b</mi><mo>-</mo><mi>λ</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="|" open="|"><mi>A</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mi>sol</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mi>λ</mi><mo>+</mo><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mi>λ</mi><mo>+</mo><mn>5</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mi>λ</mi><mo>+</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>λ</mi><mn>3</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>λ</mi><mn>2</mn></msup><mo>-</mo><mn>65</mn><mo>*</mo><mi>λ</mi><mo>+</mo><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>λ</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>λ</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>λ</mi><mo>=</mo><mn>10</mn></mtd></mtr></mtable></mfenced></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>#sol1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> C3 - JG_3 - CII Derivadas Parciales orden 3 1 - Eval1 - M Pregunta: CII Derivadas Parciales tercer orden - Eval1 - M

A partir de la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»f«/mi»«/math» encuentre la derivada parcial «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«mi»p«/mi»«/math» y evalúe en el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»0«/mn»«mo»)«/mo»«/math».

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fx</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><msup><exponentiale/><mrow><mn>2</mn><mo>·</mo><mi>x</mi></mrow></msup><mo>,</mo><mo> </mo><mi>x</mi><mo>*</mo><msup><exponentiale/><mrow><mn>2</mn><mo>·</mo><mi>x</mi></mrow></msup><mo>,</mo><mo> </mo><mi>x</mi><mo>*</mo><msup><exponentiale/><mi>x</mi></msup><mo>}</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fy</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><exponentiale/><mrow><mn>2</mn><mo>*</mo><mi>y</mi></mrow></msup><mo>,</mo><mo> </mo><msup><exponentiale/><mrow><mn>2</mn><mo>*</mo><mi>y</mi></mrow></msup><mo>,</mo><mo> </mo><mn>2</mn><mo>*</mo><msup><exponentiale/><mi>y</mi></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo> </mo><mo>=</mo><mo> </mo><mi>fx</mi><mo>*</mo><mi>fy</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>al</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>al</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>dp</mi><mo> </mo><mo>=</mo><mo> </mo><msub><mi>f</mi><mi>xxy</mi></msub></mtd></mtr><mtr><mtd><mi>dfx</mi><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>x</mi></bvar><mi>f</mi></apply></mtd></mtr><mtr><mtd><mi>dfxx</mi><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>x</mi></bvar><mi>dfx</mi></apply></mtd></mtr><mtr><mtd><mi>dfxxy</mi><mo>(</mo><mi>x</mi><mo>,</mo><mo> </mo><mi>y</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>y</mi></bvar><mi>dfxx</mi></apply></mtd></mtr><mtr><mtd><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>dfxxy</mi><mo>(</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>al</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>dp</mi><mo> </mo><mo>=</mo><mo> </mo><msub><mi>f</mi><mi>xyx</mi></msub></mtd></mtr><mtr><mtd><mi>dfx</mi><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>x</mi></bvar><mi>f</mi></apply></mtd></mtr><mtr><mtd><mi>dfxy</mi><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>y</mi></bvar><mi>dfx</mi></apply></mtd></mtr><mtr><mtd><mi>dfxyx</mi><mo>(</mo><mi>x</mi><mo>,</mo><mo> </mo><mi>y</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>x</mi></bvar><mi>dfxy</mi></apply></mtd></mtr><mtr><mtd><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>dfxyx</mi><mo>(</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>al</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>dp</mi><mo> </mo><mo>=</mo><mo> </mo><msub><mi>f</mi><mi>yxx</mi></msub></mtd></mtr><mtr><mtd><mi>dfy</mi><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>y</mi></bvar><mi>f</mi></apply></mtd></mtr><mtr><mtd><mi>dfyx</mi><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>x</mi></bvar><mi>dfy</mi></apply></mtd></mtr><mtr><mtd><mi>dfyxx</mi><mo>(</mo><mi>x</mi><mo>,</mo><mo> </mo><mi>y</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><apply><diff/><bvar><mi>y</mi></bvar><mi>dfyx</mi></apply></mtd></mtr><mtr><mtd><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>dfyxx</mi><mo>(</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> C3_JG_CII_22 Derivada Implícita 2 - M Pregunta: CII - Derivada Implícita 2 - M

Suponga que la ecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»f«/mi»«mi»d«/mi»«mi»i«/mi»«mi»s«/mi»«mi»p«/mi»«mi»l«/mi»«mi»a«/mi»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»0«/mn»«/math» definine implicitamente a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math» en una vecindad del punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»y«/mi»«mn»0«/mn»«mo»)«/mo»«/math». Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/math» en el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»y«/mi»«mn»0«/mn»«mo»)«/mo»«/math».

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alternativa</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></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>alternativa</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>x0</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>y0</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>2</mn></msqrt></mtd></mtr><mtr><mtd><mi>fdisplay</mi><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mo>)</mo><mn>2</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>F</mi><mo> </mo><mo>=</mo><mo> </mo><mi>fdisplay</mi></mtd></mtr><mtr><mtd><mi>p0</mi><mo> </mo><mo>=</mo><mo> </mo><mn>36</mn></mtd></mtr><mtr><mtd><mi>dyx</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mfrac><apply><diff/><bvar><mi>x</mi></bvar><mi>F</mi></apply><apply><diff/><bvar><mi>y</mi></bvar><mi>F</mi></apply></mfrac></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>dyx</mi><mo>(</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>alternativa</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>x0</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>y0</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>p0</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>fdisplay</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>8</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></mrow></mfrac><mo>+</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>4</mn></msup></mtd></mtr><mtr><mtd><mi>F</mi><mo> </mo><mo>=</mo><mo> </mo><mi>fdisplay</mi></mtd></mtr><mtr><mtd><mi>dyx</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mfrac><apply><diff/><bvar><mi>x</mi></bvar><mi>F</mi></apply><apply><diff/><bvar><mi>y</mi></bvar><mi>F</mi></apply></mfrac></mtd></mtr><mtr><mtd><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>dyx</mi><mo>(</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>alternativa</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>x0</mi><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>y0</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>p0</mi><mo> </mo><mo>=</mo><mo> </mo><mn>6</mn></mtd></mtr><mtr><mtd><mi>fdisplay</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mrow><mn>5</mn><mo>-</mo><mi>y</mi></mrow></msqrt><mo>+</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>F</mi><mo> </mo><mo>=</mo><mo> </mo><mi>fdisplay</mi></mtd></mtr><mtr><mtd><mi>dyx</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mfrac><apply><diff/><bvar><mi>x</mi></bvar><mi>F</mi></apply><apply><diff/><bvar><mi>y</mi></bvar><mi>F</mi></apply></mfrac></mtd></mtr><mtr><mtd><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>dyx</mi><mo>(</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> C3_JG_CII_24 Determinante 6- M Pregunta: CII - Determinante 6 - M

Calcular el determinante de la matriz «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»A«/mi»«/math».

Dada la matriz:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»A«/mi»«/math»

Calcular el determinante de la matriz A.