MATE GGZZ II/2. Gaia-Determinanteak Ariketa_1 Kalkula itzazu matrize hauen determinanteak:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»C«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»D«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»E«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/mtd»«mtd»«mi»m«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A= #r1B= #r2C= #r3D= #r4E= #r5]]> <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>r1</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>5</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mo>-</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>b</mi></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r5</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><msup><mi>m</mi><mn>2</mn></msup></mtd><mtd><mi>m</mi></mtd></mtr><mtr><mtd><mi>m</mi></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command></group></library><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"><mfenced open="|" close="|"><mi>A</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><mfenced open="|" close="|"><mi>B</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><mfenced open="|" close="|"><mi>C</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>3</mn><mspace linebreak="newline"/><mfenced open="|" close="|"><mi>D</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>4</mn><mspace linebreak="newline"/><mfenced open="|" close="|"><mi>E</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>5</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_10 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»c«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»d«/mi»«/mtd»«mtd»«mi»e«/mi»«/mtd»«mtd»«mi»f«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»g«/mi»«/mtd»«mtd»«mi»h«/mi»«/mtd»«mtd»«mi»i«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mn»3«/mn»«/mstyle»«/math» dela jakinik, kalkulatu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mi»i«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»g«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»h«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»f«/mi»«mo»+«/mo»«mi»c«/mi»«/mtd»«mtd»«mi»d«/mi»«mo»+«/mo»«mi»a«/mi»«/mtd»«mtd»«mi»e«/mi»«mo»+«/mo»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«mi»c«/mi»«/mtd»«mtd»«mn»3«/mn»«mi»a«/mi»«/mtd»«mtd»«mn»3«/mn»«mi»b«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Emaitza  : {#1}

]]> 1.0000000 0.3333333 0 <question/> Ariketa_11  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mi»d«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»e«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»f«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mi»a«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»b«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»c«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mi»g«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»h«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»i«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mn»100«/mn»«/mstyle»«/math» dela jakinik, kalkulatu  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«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»«/mstyle»«/math»

Emaitza  : {#1}

]]> 1.0000000 0.3333333 0 <question/> Ariketa_12_1 Ebatzi ondorengo ekuazioa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mi»x«/mi»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mn»0«/mn»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 x= #r1]]> <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>S</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">3</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">3</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">4</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">7</mn></mtd></mtr></mtable></mfenced><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">=</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><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>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_12_2 Ebatzi ondorengo ekuazioa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mi»x«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mi»x«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mn»2«/mn»«/mstyle»«/math»

Sartu balioak txienetik handienera.

]]> 1.0000000 0.3333333 0 0 x1= #r1x2= #r2]]> <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>S</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">4</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd></mtr></mtable></mfenced><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">=</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>minimo</mi><mo>(</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mi>S</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>maximo</mi><mo>(</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mi>S</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_13  Kalkula ezazu  determinantea a, b  eta  c-ren arabera.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»c«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mi»b«/mi»«mo»+«/mo»«mn»2«/mn»«/mtd»«mtd»«mi»c«/mi»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«mo»+«/mo»«mn»1«/mn»«/mtd»«mtd»«mi»b«/mi»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mi»c«/mi»«mo»+«/mo»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A=#r1]]> <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>r1</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>a</mi><mo>-</mo><mn>1</mn></mtd><mtd><mi>b</mi><mo>+</mo><mn>2</mn></mtd><mtd><mi>c</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>+</mo><mn>1</mn></mtd><mtd><mi>b</mi><mo>-</mo><mn>3</mn></mtd><mtd><mi>c</mi><mo>+</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></input></command></group></library><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"><mfenced open="|" close="|"><mi>A</mi></mfenced><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_14_1 Aurkitu matrize honen alderantzizkoa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A-1=#r1]]> <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>r1</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_14_2 Aurkitu matrize honen alderantzizkoa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced»«mtable»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A-1=#r1]]> <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>r1</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_14_3 Aurkitu matrize honen alderantzizkoa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A-1=#r1]]> <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>r1</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_14_4 Aurkitu matrize honen alderantzizkoa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A-1=#r1]]> <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>r1</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_15  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» matrizeak emanik, kalkulatu bere alderantzizkoa eta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup»«mi»A«/mi»«mn»5«/mn»«/msup»«/mstyle»«/math».

]]> 1.0000000 0.3333333 0 0 A-1=#r1A5=#r2]]> <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>r1</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mn>5</mn></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>A</mi><mn>5</mn></msup><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_18 Ebatzi ondorengo ekuazioa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mi»x«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»8«/mn»«/mtd»«mtd»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mn»67«/mn»«/mstyle»«/math»

Sartu balioak txienetik handienera.

]]> 1.0000000 0.3333333 0 0 x1= #r1x2= #r2]]> <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>S</mi><mo>=</mo><mi>resolver</mi><mfenced><mrow><mfenced close="|" open="|"><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>2</mn><mo>*</mo><mi>x</mi></mtd></mtr><mtr><mtd><mn>8</mn></mtd><mtd><mi>x</mi><mo>-</mo><mn>1</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mn>67</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>minimo</mi><mo>(</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mi>S</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>maximo</mi><mo>(</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mi>S</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_2_1 Kalkula itzazu matrize hauen determinanteak:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»C«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A= #r1B= #r2C= #r3]]> <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>r1</mi><mo>=</mo><mo style="font-family:SansSerif;font-size:14px;font-weight:bold"> </mo><mfenced close="|" open="|" style="font-family:SansSerif;font-size:14px;font-weight:bold"><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo style="font-family:SansSerif;font-size:14px;font-weight:bold"> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>5</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>5</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math></input></command></group></library><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"><mfenced open="|" close="|"><mi>A</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><mfenced open="|" close="|"><mi>B</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><mfenced open="|" close="|"><mi>C</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_2_2 Kalkula itzazu matrize hauen determinanteak:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mi»a«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mi»m«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»C«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»m«/mi»«mo»+«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mi»m«/mi»«mo»+«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mi»m«/mi»«mo»+«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A= #r1B= #r2C= #r3]]> <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>r1</mi><mo>=</mo><mo style="font-family:SansSerif;font-size:14px;font-weight:bold"> </mo><mfenced close="|" open="|" style="font-family:SansSerif;font-size:14px;font-weight:bold"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mi>a</mi></mtd></mtr></mtable></mfenced><mo style="font-family:SansSerif;font-size:14px;font-weight:bold"> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>m</mi></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mi>m</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>m</mi><mo>+</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>m</mi><mo>+</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mi>m</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math></input></command></group></library><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"><mfenced open="|" close="|"><mi>A</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><mfenced open="|" close="|"><mi>B</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><mfenced open="|" close="|"><mi>C</mi></mfenced><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_20_1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» matrizea emanik

"m"_ren zein balioentzat egongo da A_ren alderantzizkoa?

m {#1}  {#2}_rentzat

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>5</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><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="casSession"/></localData></question> Ariketa_20_2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»  matrizea emanik, kalkulatu alderantzizkoa «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»m«/mi»«mo»=«/mo»«mn»1«/mn»«/mstyle»«/math»_entzat.

]]> 1.0000000 0.3333333 0 0 A-1=#r2]]> <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>r1</mi><mo>=</mo><mi>a</mi><mo>≠</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>5</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_22_1  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mi»m«/mi»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» matrizea emanik

"m"_ren zein balioentzat ez du A matrizeak alderantzizkoa?

Sartu lehenengo balio txikiena

m  {#1}   {#2} eta {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>m</mi></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mi>m</mi></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>minimo</mi><mo>(</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>m</mi><mo>)</mo><mo>,</mo><msub><mi>S</mi><mn>2</mn></msub><mo>(</mo><mi>m</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>maximo</mi><mo>(</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>m</mi><mo>)</mo><mo>,</mo><msub><mi>S</mi><mn>2</mn></msub><mo>(</mo><mi>m</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><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="casSession"/></localData></question> Ariketa_22_2  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mi»m«/mi»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» matrizea emanik, kalkulatu alderantzizkoa «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»m«/mi»«mo»=«/mo»«mn»2«/mn»«/mstyle»«/math»_rentzat.

]]> 1.0000000 0.3333333 0 0 A-1=#r2]]> <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>r2</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_23_1  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mi»m«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mi»m«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» matrizea emanik

"m"_ren zein balioentzat ez du A matrizeak alderantzizkorik?

Sartu lehenengo balio txikiena

 m  {#1}     {#2}_rentzat

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">m</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">m</mi></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><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="casSession"/></localData></question> Ariketa_23_2  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn style=¨font-family:SansSerif¨»1«/mn»«/mtd»«mtd»«mn style=¨font-family:SansSerif¨»1«/mn»«/mtd»«mtd»«mi style=¨font-family:SansSerif¨»m«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn style=¨font-family:SansSerif¨»0«/mn»«/mtd»«mtd»«mo style=¨font-family:SansSerif¨»-«/mo»«mn style=¨font-family:SansSerif¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo style=¨font-family:SansSerif¨»-«/mo»«mi style=¨font-family:SansSerif¨»m«/mi»«/mtd»«mtd»«mo style=¨font-family:SansSerif¨»-«/mo»«mn style=¨font-family:SansSerif¨»1«/mn»«/mtd»«mtd»«mn style=¨font-family:SansSerif¨»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»  matrizea emanik,  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»m«/mi»«mo»=«/mo»«mn»2«/mn»«/mstyle»«/math» izanik ,kalkulatu, ahal bada X matrizea, ondorengo berdintza bete daiten. Kalkulatu lehenik A_ren alderantzizkoa.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»X«/mi»«mo»§#183;«/mo»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A-1= #r2X= #r1]]> <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>r1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>*</mo><msup><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><mi>X</mi><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_24  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» matrizea emanik:

  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»A«/mi»«mo»-«/mo»«mi»I«/mi»«/mrow»«/mstyle»«/math» matrizearen alderantzizkoa kalkulatu,I2 ordeneko identitate matrizea izanik.
  • Kalkulatu B matrizea  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»+«/mo»«mi»B«/mi»«mo»=«/mo»«mi»A«/mi»«mo»§#183;«/mo»«mi»B«/mi»«/mstyle»«/math» betetzen duena

 

]]> 1.0000000 0.3333333 0 0 A-I -1= #r1B= #r2]]> <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>r1</mi><mo>=</mo><msup><mfenced><mrow><mfenced><mtable><mtr><mtd><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced><mo>-</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mfenced><msup><mfenced><mrow><mfenced><mtable><mtr><mtd><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced><mo>-</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></mfenced><mo>*</mo><mfenced><mtable><mtr><mtd><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></input></command></group></library><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"><msup><mfenced><mrow><mi>A</mi><mo>-</mo><mi>I</mi><mo>&#160;</mo></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><mi>B</mi><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_4 Kalkula ezazu  determinantea a, b  eta  c-ren arabera.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«mo»+«/mo»«mi»b«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»a«/mi»«mo»+«/mo»«mi»c«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 A=#r1]]> <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>r1</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">+</mo><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">+</mo><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">c</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><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"><mfenced open="|" close="|"><mi>A</mi></mfenced><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_5_1 Ondorengo matrizea emanik:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Kalkulatu   a11 , a23 , a32 , a12  elementuen minore osagarria.

]]> 1.0000000 0.3333333 0 0 α11= #r1α23= #r2α32= #r3α12= #r4]]> <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>r1</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn></mrow></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&#945;</mi><mn>11</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>&#945;</mi><mn>23</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><msub><mi>&#945;</mi><mn>32</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>3</mn><mspace linebreak="newline"/><msub><mi>&#945;</mi><mn>12</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_5_2 Ondorengo matrizea emanik:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Kalkulatu   a11  , a12  elementuen minore osagarria.

]]> 1.0000000 0.3333333 0 0 α11= #r1α12= #r4]]> <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>r1</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&#945;</mi><mn>11</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>&#945;</mi><mn>12</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_5_3 Ondorengo matrizea emanik:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»c«/mi»«/mtd»«mtd»«mi»d«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»c«/mi»«/mtd»«mtd»«mi»d«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Kalkulatu   a11 , a23 , a32 , a12  elementuen minore osagarria.

]]> 1.0000000 0.3333333 0 0 α11= #r1α23= #r2α32= #r3α12= #r4]]> <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>r1</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn></mrow></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&#945;</mi><mn>11</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>&#945;</mi><mn>23</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><msub><mi>&#945;</mi><mn>32</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>3</mn><mspace linebreak="newline"/><msub><mi>&#945;</mi><mn>12</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_5_4 Ondorengo matrizea emanik:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Kalkulatu   a11 , a23 , a32 , a12  elementuen adjuntoa.

]]> 1.0000000 0.3333333 0 0 A11= #r1A23= #r2A32= #r3A12= #r4]]> <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>r1</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mo>-</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>-</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn></mrow></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mo>-</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mn>11</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>A</mi><mn>23</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><msub><mi>A</mi><mn>32</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>3</mn><mspace linebreak="newline"/><msub><mi>A</mi><mn>12</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_5_5 Ondorengo matrizea emanik:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Kalkulatu   a11 ,  a12  elementuen adjuntoa.

]]> 1.0000000 0.3333333 0 0 A11= #r1A12= #r4]]> <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>r1</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mo>-</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mn>11</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>A</mi><mn>12</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_5_6 Ondorengo matrizea emanik:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»c«/mi»«/mtd»«mtd»«mi»d«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mo»-«/mo»«mi»c«/mi»«/mtd»«mtd»«mi»d«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Kalkulatu   a11 , a23 , a32 , a12  elementuen adjuntoa.

]]> 1.0000000 0.3333333 0 0 A11= #r1A23= #r2A32= #r3A12= #r4]]> <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>r1</mi><mo>=</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mo>-</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>-</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn></mrow></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mo>-</mo><mi>menor</mi><mfenced><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><msup><mi>a</mi><mn>2</mn></msup></mtd><mtd><mi>b</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mn>11</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>A</mi><mn>23</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><msub><mi>A</mi><mn>32</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>3</mn><mspace linebreak="newline"/><msub><mi>A</mi><mn>12</mn></msub><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_7_1 Kalkula ezazu matrize honen matrize adjuntua

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 Aadj = #r1]]> <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>r1</mi><mo>=</mo><msup><mfenced><mrow><mi>matriz_adjunta</mi><mfenced><mtable><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">4</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>T</mo></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mi>a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">j</mi></mrow></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_7_2 Kalkula ezazu matrize honen matrize adjuntua

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 Aadj = #r1]]> <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>r1</mi><mo>=</mo><msup><mfenced><mrow><mi>matriz_adjunta</mi><mfenced><mtable><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">3</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">3</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">5</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">5</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">4</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>T</mo></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mi>a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">j</mi></mrow></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_7_3 Kalkula ezazu matrize honen matrize adjuntua

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mi»c«/mi»«/mtd»«mtd»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mi»a«/mi»«/mtd»«mtd»«mi»c«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mi»c«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 Aadj = #r1]]> <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>r1</mi><mo>=</mo><msup><mfenced><mrow><mi>matriz_adjunta</mi><mfenced><mtable><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">c</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">a</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">c</mi></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">b</mi></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">c</mi></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>T</mo></msup></math></input></command></group></library><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"><msup><mi>A</mi><mrow><mi>a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">j</mi></mrow></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa_8  Jakina da «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mfenced open=¨|¨ close=¨|¨»«mi»A«/mi»«/mfenced»«mo»=«/mo»«mn»5«/mn»«/mrow»«/mstyle»«/math» dela eta A matrizearen ordena bi dela. Zenbat balio du «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mn»3«/mn»«mi»A«/mi»«/mrow»«/mfenced»«/mstyle»«/math»?  {#1}

Bi matrize A eta B alderantzizkoak dira. A-ren determinantearen balioa 3 bada, zenbat balio du B-ren determinanteak?  {#2}

]]> 2.0000000 0.3333333 0 <question/> Ariketa_9_1 Kalkulatu ondorengo determinantea:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»6«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #r1 <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>r1</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">3</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">5</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">5</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">0</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">3</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">5</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">6</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">3</mn></mtd></mtr><mtr><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">3</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">2</mn></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r1</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_9_2 Kalkulatu ondorengo determinantea:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mi»x«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mi»x«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mi»x«/mi»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mi»x«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #r1 <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>r1</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd><mtd><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd></mtr><mtr><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mo style="font-family:SansSerif;font-size:14px;font-weight:bold">-</mo><mn style="font-family:SansSerif;font-size:14px;font-weight:bold">1</mn></mtd><mtd><mi style="font-family:SansSerif;font-size:14px;font-weight:bold">x</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r1</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ariketa_9_3 Kalkulatu ondorengo matrizearen determinantea:

#det

]]> 1.0000000 0.3333333 0 0 #r1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>det</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mfenced close="|" open="|"><mi>det</mi></mfenced></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>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>708</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r1</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>