<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>Vector_Dependent_1</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Find \(\alpha\) such that the set of vectors \[ { {@c1@},\ {@c2@},\ {@c3@} } \] is linearly dependent. <br /> [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>For the vectors to be linearly dependent the determinant of the matrix of vectors must equal zero. So for the vectors \[{@matrixc123@}\] The determinant is \[{@detmatrix@} = 0.\] Hence \[{@detmatrixsimp@} =0,\] and therefore \[\alpha = {@correctanswer@}\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>s1:rand(9)+1;
 s2:rand(9)+1;
 s3:-(rand(9)+1);
 n1:rand(5)+1;
 n2:rand_with_step(-5,1,1);
 n3:rand(3)+1;
 c1:matrix([1],[s1],[s2]);
 c2:matrix([2],[11],[s3]);
 c3:ev(n1*c1+n2*c2);
 correctanswer:c3[n3,1];
 c3[n3,1]:alpha;
 matrixc123:matrix([c1[1,1],c1[2,1],c1[3,1]],[c2[1,1],c2[2,1],c2[3,1]],[c3[1,1],c3[2,1],c3[3,1]]);
  detmatrix:determinant(matrixc123);
  detmatrixsimp:expand(detmatrix);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\( {@matrixc123@}\) linearly dependent gives \(\alpha = {@correctanswer@}\)</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</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>
      <showvalidation>1</showvalidation>
      <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</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>Result-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>773676505</deployedseed>
    <deployedseed>105749905</deployedseed>
    <deployedseed>1711187603</deployedseed>
    <deployedseed>803057932</deployedseed>
    <deployedseed>361988814</deployedseed>
    <deployedseed>89180014</deployedseed>
    <deployedseed>1305919914</deployedseed>
    <deployedseed>1189020386</deployedseed>
    <deployedseed>632343148</deployedseed>
    <deployedseed>1447152166</deployedseed>
    <deployedseed>1791978376</deployedseed>
    <deployedseed>1122023735</deployedseed>
    <deployedseed>627041222</deployedseed>
    <deployedseed>1712072895</deployedseed>
    <deployedseed>1467012576</deployedseed>
    <deployedseed>789457941</deployedseed>
    <deployedseed>1904040348</deployedseed>
    <deployedseed>1006961264</deployedseed>
    <deployedseed>81146575</deployedseed>
    <deployedseed>943146373</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>correctanswer</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>correctanswer-1</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
