<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>Matrices_4</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>If a {@n1@} by {@n1@} matrix \({\bf A}\) has \(\det({\bf A}) = {@a1@}\), find \[\det({@a2@}{\bf A}),\det({@a3@}{\bf A}),\det({\bf A}^{@a4@}),\det(({\bf A}^{-1})^{@-a5@})\] <br /> Enter your answers in the right order in the boxes below.</p>
<p>\(\det({@a2@}{\bf A}) = \) [[input:ans1]][[validation:ans1]] <br /> \(\det({@a3@}{\bf A}) = \) [[input:ans2]][[validation:ans2]] <br /> \(\det({\bf A}^{@a4@}) = \) [[input:ans3]][[validation:ans3]] <br /> \(\det({\bf A}^{-1})^{@-a5@}) = \) [[input:ans4]][[validation:ans4]]</p>
<p> </p>
<p> </p>
<p> </p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>If a \({@n1@}\) by \({@n1@}\) matrix \({\bf A}\) has \(\det({\bf A}) = {@a1@}\), then \[\det({@a2@}{\bf A}) = {@a2@}^{@n1@}\cdot{@a1@} = {@a2^(n1)*a1@}\] <br /> \[\det(\{@a3@}{\bf A}) = ({@a3@})^{@n1@}\cdot{@a1@} = {@a3^(n1)*a1@}\] <br /> \[\det({\bf A}^{@a4@})= ({@a1@})^{@a4@} = {@a1^a4@}\] <br /> \[\det(({\bf A}^{-1})^{@-a5@}) ={@a1@}^{@a5@} = {@a1^a5@}\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>n1:rand(3)+3;
  a1:rand(2)+2;
  a2:rand(4)+2;
  a3:-(rand(4)+2);
  a4:rand(3)+2;
  a5:-(rand(4)+2);
  correctanswer:[a1*(a2)^n1, a1*(a3)^n1, a1^a4, a1^a5];
  wronganswer1:[-a1*(a2)^n1, a1*(a3)^n1, a1^a4, a1^a5];
  wronganswer2:[a1*(a2)^n1, -a1*(a3)^n1, a1^a4, a1^a5];
  wronganswer3:[a1*(a2)^n1, a1*(a3)^n1, -a1^a4, -a1^a5];
  wronganswer4:[a1*(a2)^n1, a1*(a3)^n1, a1^a4, -a1^a5];</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>For a {@n1@} by {@n1@} matrix with \(\det({\bf A}) = {@a1@}, \det({@a2@}{\bf A}),\det({@a3@}{\bf A}),\det({\bf A}^{@a4@}),\det(({\bf A}^{-1})^{@-a5@})\) 
   gives {@correctanswer@}</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <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>correctanswer[1]</tans>
      <boxsize>20</boxsize>
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      <mustverify>1</mustverify>
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      <options/>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>correctanswer[2]</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
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      <options/>
    </input>
    <input>
      <name>ans3</name>
      <type>algebraic</type>
      <tans>correctanswer[3]</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
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      <forbidwords>determinant</forbidwords>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans4</name>
      <type>algebraic</type>
      <tans>correctanswer[4]</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>determinant</forbidwords>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
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      <options/>
    </input>
    <prt>
      <name>Result</name>
      <value>2.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>correctanswer[1]</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
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        <trueanswernote>Result-0-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>\(\det({@a2@}{\bf A})\) is correct.</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>Result-0-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>\(\det({@a2@}{\bf A})\) is incorrect.</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans2</sans>
        <tans>correctanswer[2]</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.2500000</truescore>
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        <truenextnode>2</truenextnode>
        <trueanswernote>Result-1-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>\(\det({@a3@}{\bf A})\) is correct.</p>]]></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>Result-1-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>\(\det({@a3@}{\bf A})\) is incorrect.</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans3</sans>
        <tans>correctanswer[3]</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.2500000</truescore>
        <truepenalty/>
        <truenextnode>3</truenextnode>
        <trueanswernote>Result-2-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>\(\det\,({\bf A}^{@a4@})\) is correct.</p>]]></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>3</falsenextnode>
        <falseanswernote>Result-2-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>\(\det\,({\bf A}^{@a4@})\) is incorrect.</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>3</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans4</sans>
        <tans>correctanswer[4]</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.2500000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-3-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>\(\det\,(({\bf A}^{-1})^{@-a5@})\) is correct.</p>]]></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>Result-3-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>\(\det\,(({\bf A}^{-1})^{@-a5@})\) is incorrect.</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>correctanswer[1]</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>correctanswer[2]</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>correctanswer[3]</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>correctanswer[4]</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-3-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>correctanswer[1] -10</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>correctanswer[2]-10</value>
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      <testinput>
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        <value>correctanswer[3]-10</value>
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        <name>ans4</name>
        <value>correctanswer[4]-10</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-3-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>wronganswer1[1]</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>wronganswer1[2]</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>wronganswer1[3]</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>wronganswer1[4]</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.7500000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-3-T</expectedanswernote>
      </expected>
    </qtest>
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      <testcase>4</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
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        <value>wronganswer2[2]</value>
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      <testinput>
        <name>ans3</name>
        <value>wronganswer2[3]</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>wronganswer2[4]</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.7500000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-3-T</expectedanswernote>
      </expected>
    </qtest>
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      <testcase>5</testcase>
      <description/>
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        <name>ans1</name>
        <value>wronganswer3[1]</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>wronganswer3[2]</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>wronganswer3[3]</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>wronganswer3[4]</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-3-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>6</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>wronganswer4[1]</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>wronganswer4[2]</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>wronganswer4[3]</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>wronganswer4[4]</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.7500000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-3-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
