1 Linear Algebra/1.1.12 Linear equations systems
Linear equations systems 2
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#LS1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#LS2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#LS3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»
which is the associated single matrix equation «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»·«/mo»«mi»x«/mi»«mo»=«/mo»«mi»b«/mi»«/math»?
]]>
1.0000000
0.1000000
0
0
A=#Ab=#b ]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>a2</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>a3</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>b2</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>b3</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>c2</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>;</mo><mi>c3</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>s</mi><mo>:</mo><mo>=</mo></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></mtd></mtr></mtable></mfenced><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>·</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mn>0</mn></mtd></mtr></mtable></mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn></mtd></mtr></mtable></mfenced></apply></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c1</mi><mo>·</mo><mi>z</mi><mo>=</mo><msub><mi>s</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c2</mi><mo>·</mo><mi>z</mi><mo>=</mo><msub><mi>s</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS3</mi><mo>=</mo><mi>a3</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b3</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c3</mi><mo>·</mo><mi>z</mi><mo>=</mo><msub><mi>s</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a1</mi></mtd><mtd><mi>b1</mi></mtd><mtd><mi>c1</mi></mtd></mtr><mtr><mtd><mi>a2</mi></mtd><mtd><mi>b2</mi></mtd><mtd><mi>c2</mi></mtd></mtr><mtr><mtd><mi>a3</mi></mtd><mtd><mi>b3</mi></mtd><mtd><mi>c3</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msup><mfenced close="]" open="["><mrow><msub><mi>s</mi><mn>1</mn></msub><mo>,</mo><msub><mi>s</mi><mn>2</mn></msub><mo>,</mo><msub><mi>s</mi><mn>3</mn></msub></mrow></mfenced><mo>T</mo></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LS3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>5</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>7</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo>#</mo><mi>A</mi><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo>#</mo><mi>b</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>