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<quiz>
  <question type="stack">
    <name>
      <text>7.3.1.2 Task: compute these 2x2 determinants</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Evaluate the determinants of the following matrices.</p>
<ol class="HELM_parts_inline">
<li>\(A={@matrixa@}\)</li>
<li>\(B={@matrixb@}\)</li>
<li>\(C={@matrixc@}\)</li></ol>

<ol class="HELM_parts">

<li><p>\(\det{A}=\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p></li>

<li><p>\(\det{B}=\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p></li>

<li><p>\(\det{C}=\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p></li>

</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We use the definition to find the determinant of the following matrices.</p>
<ol class="HELM_parts">
  <li><p>For \(A={@matrixa@},\)</p>
    <p>\(\det(A) = {@detAA@} = {@ta1@}.\)</p>
    </li>
    <li><p>For \(B={@matrixb@},\)</p>
      <p>\(\det(B) = {@detBB@} = {@ta2@}.\)</p>
    </li>
    <li><p>For \(C={@matrixc@},\)</p>
      <p>\(\det(C) = {@detCC@} = {@ta3@}.\)</p>
  </li>
</ol>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2021072200</text>
    </stackversion>
    <questionvariables>
      <text>matrixa: matrix([rand_with_step(-5,5,1),rand_with_step(-5,5,1)],[rand_with_step(-5,5,1),rand_with_step(-5,5,1)]);
matrixb: ev(matrixa,simp);
matrixb: matrix([rand_with_step(-5,5,1),0],[rand_with_step(-5,5,1),rand_with_step(-5,5,1)]);
matrixb: ev(matrixb,simp);
c1 : rand_with_step(-5,5,1);
c2 : rand_with_step(-5,5,1);
co1 : 2+rand(4);
co2 : rand_with_step(-5,5,1);
matrixc: matrix([co1*c1,co2*c1],[co1*c2,co2*c2]);
matrixc: ev(matrixc,simp);
ta1: ev(determinant(matrixa),simp);
ta2: ev(determinant(matrixb),simp);
ta3: ev(determinant(matrixc),simp);
AA: matrixa;
BB: matrixb;
CC: matrixc;
detAA: unary_minus_sort(AA[1,1]*AA[2,2]-AA[1,2]*AA[2,1]);
detBB: unary_minus_sort(BB[1,1]*BB[2,2]-BB[1,2]*BB[2,1]);
detCC: unary_minus_sort(CC[1,1]*CC[2,2]-CC[1,2]*CC[2,1]);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(A = {@matrixa@}\),\(B = {@matrixb@}\),\(C = {@matrixc@}\)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>0</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>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>4</boxsize>
      <strictsyntax>1</strictsyntax>
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      <options/>
    </input>
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      <name>ans2</name>
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      <tans>ta2</tans>
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      <strictsyntax>1</strictsyntax>
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    </input>
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      <tans>ta3</tans>
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    <qtest>
      <testcase>1</testcase>
      <description/>
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        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ta3</value>
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        <name>prt2</name>
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        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
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        <name>prt3</name>
        <expectedscore>1.0000000</expectedscore>
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      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
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        <name>ans1</name>
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      </testinput>
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        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
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        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
