<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>Vector_1</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Let \({\bf v_{1}}\) and \({\bf v_2}\) be the following vectors: <br /> \[ {\bf v_{1}} = {@c1@}, {\bf v_{2}} = {@c2@}.\] <br /> Compute \[ {@a1@} {\bf v_1} + {@b1@} {\bf v_2} .\] <br /> [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Given \[ {\bf v_{1}} = {@c1@}, {\bf v_{2}} = {@c2@}.\] <br /> \[ {@a1@} {\bf v_1} + {@b1@} {\bf v_2} = {@a1@}{@c1@}+{@b1@}{@c2@}\] \[ = {@vmult1@} + {@vmult2@} = {@correctanswer@}\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>Au:matrix([rand_with_step(-1,1,2),ev(rand(9)-4),ev(rand(9)-4)],[0,rand_with_step(-1,1,2),ev(rand(9)-4)],[0,0,rand_with_step(-1,1,2)]);
 Bu:matrix([rand_with_step(-1,1,2),ev(rand(9)-4),ev(rand(9)-4)],[0,rand_with_step(-1,1,2),ev(rand(9)-4)],[0,0,rand_with_step(-1,1,2)]);
 Amat:ev(transpose(Au) . Bu);
 c1:col(Amat,1);
 c2:col(Amat,2);
 a1:rand(8)+ 2;
 b1:rand(8)+ 2;
 correctanswer:a1*c1+b1*c2;
 wronganswer:(a1-1)*c1+(b1-1)*c2;
 vmult1:matrix([0],[0],[0]);
 vmult1[1,1]:a1*c1[1,1];
 vmult1[2,1]:a1*c1[2,1];
 vmult1[3,1]:a1*c1[3,1];
 vmult2:matrix([0],[0],[0]);
 vmult2[1,1]:b1*c2[1,1];
 vmult2[2,1]:b1*c2[2,1];
 vmult2[3,1]:b1*c2[3,1];</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\( {@a1@} {@c1@} + {@b1@} {@c2@}\) 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>matrix</type>
      <tans>correctanswer</tans>
      <boxsize>10</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>Result</name>
      <value>1.0000000</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>294285686</deployedseed>
    <deployedseed>2053539169</deployedseed>
    <deployedseed>151189632</deployedseed>
    <deployedseed>361951778</deployedseed>
    <deployedseed>1156812808</deployedseed>
    <deployedseed>541921123</deployedseed>
    <deployedseed>1076970528</deployedseed>
    <deployedseed>782495567</deployedseed>
    <deployedseed>105552620</deployedseed>
    <deployedseed>508428852</deployedseed>
    <deployedseed>606452657</deployedseed>
    <deployedseed>1814880386</deployedseed>
    <deployedseed>687453788</deployedseed>
    <deployedseed>949284973</deployedseed>
    <deployedseed>1077558460</deployedseed>
    <deployedseed>924485479</deployedseed>
    <deployedseed>294595968</deployedseed>
    <deployedseed>1972824967</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>wronganswer</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
