<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>PT.7.2 (Write sim. eqns. with matrices)</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<p>Write the following system of linear equations as a matrix equation.
\[
\begin{align*}
&{@a1@}x_1 + {@a2@}x_2 + {@a3@}x_3 = {@b1@}
\\
&{@a4@}x_1 + {@a5@}x_2 + {@a6@}x_3 = {@b2@}
\\
&{@a7@}x_1 + {@a8@}x_2 + {@a9@}x_3 = {@b3@}
\end{align*}
\]</p>

<ul style="list-style-type:none;">
<li>
[[input:ans1]] [[validation:ans1]] \(\begin{bmatrix}
x_1
\\
x_2
\\
x_3
\end{bmatrix} = \)[[input:ans2]] [[validation:ans2]]
</li>]]></text>
    </questiontext>
    <generalfeedback format="moodle_auto_format">
      <text><![CDATA[<p>We can use matrices to write this equation in the form \(A \mathbf{x} = \mathbf{b}\).  So the coefficients of each \(x_i\) are the entries of the matrix \(A\) and the entries of the vector \(\mathbf{b}\) are the values on the right hand side of the equals sign. So we have 
\[
{@ta1@} \begin{bmatrix}
x_1
\\
x_2
\\
x_3
\end{bmatrix} = {@ta2@}.
\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>a1: 1+rand(5);
a2: 1+rand(5);
a3: 1+rand(5);
a4: 1+rand(5);
a5: 1+rand(5); 
a6: 1+rand(5);
a7: 1+rand(5);
a8: 1+rand(5);
a9: 1+rand(5);

b1: 1+rand(10);
b2: 1+rand(10);
b3: 1+rand(10);

ta1: matrix([a1,a2,a3],[a4,a5,a6],[a7,a8,a9]);
ta2: matrix([b1],[b2],[b3]);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\({@ta1@} \begin{bmatrix}
x_1
\\
x_2
\\
x_3
\end{bmatrix} {@ta2@}\)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
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    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
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    <variantsselectionseed/>
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      <name>ans1</name>
      <type>matrix</type>
      <tans>ta1</tans>
      <boxsize>5</boxsize>
      <strictsyntax>1</strictsyntax>
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      <showvalidation>3</showvalidation>
      <options/>
    </input>
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      <name>ans2</name>
      <type>matrix</type>
      <tans>ta2</tans>
      <boxsize>5</boxsize>
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    </input>
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          <text/>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-2-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
