0004.qti

<item ident="G1-0004" title="G1 | Row operations and determinants | ver. 0004">
  <itemmetadata>
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        <fieldlabel>question_type</fieldlabel>
        <fieldentry>essay_question</fieldentry>
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  <presentation>
    <material>
      <mattextxml>
        <div class="exercise-statement">
          <p>
            <strong>G1.</strong>
          </p>
          <p>Let <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"/> be a <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4 \times 4" alt="4 \times 4" title="4 \times 4" data-latex="4 \times 4"/> matrix with determinant <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?6" alt="6" title="6" data-latex="6"/>.</p>
          <ol type="a">
            <li>Let <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?N" alt="N" title="N" data-latex="N"/> be the matrix obtained from <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"/> by applying the row operation <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_3 \to -3R_3" alt="R_3 \to -3R_3" title="R_3 \to -3R_3" data-latex="R_3 \to -3R_3"/>. What is <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ N" alt="\operatorname{det}\ N" title="\operatorname{det}\ N" data-latex="\operatorname{det}\ N"/>?</li>
            <li>Let <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?Q" alt="Q" title="Q" data-latex="Q"/> be the matrix obtained from <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"/> by applying the row operation <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_1 \leftrightarrow R_2" alt="R_1 \leftrightarrow R_2" title="R_1 \leftrightarrow R_2" data-latex="R_1 \leftrightarrow R_2"/>. What is <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ Q" alt="\operatorname{det}\ Q" title="\operatorname{det}\ Q" data-latex="\operatorname{det}\ Q"/>?</li>
            <li>Let <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?C" alt="C" title="C" data-latex="C"/> be the matrix obtained from <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"/> by applying the row operation <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_1 \to R_1 + 5R_2" alt="R_1 \to R_1 + 5R_2" title="R_1 \to R_1 + 5R_2" data-latex="R_1 \to R_1 + 5R_2"/>. What is <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ C" alt="\operatorname{det}\ C" title="\operatorname{det}\ C" data-latex="\operatorname{det}\ C"/>?</li>
          </ol>
        </div>
      </mattextxml>
      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;G1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Let &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"&gt; be a &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4%20%5Ctimes%204" alt="4 \times 4" title="4 \times 4" data-latex="4 \times 4"&gt; matrix with determinant &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?6" alt="6" title="6" data-latex="6"&gt;.&lt;/p&gt;
  &lt;ol type="a"&gt;
    &lt;li&gt;Let &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?N" alt="N" title="N" data-latex="N"&gt; be the matrix obtained from &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"&gt; by applying the row operation &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_3%20%5Cto%20-3R_3" alt="R_3 \to -3R_3" title="R_3 \to -3R_3" data-latex="R_3 \to -3R_3"&gt;. What is &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Coperatorname%7Bdet%7D%5C%20N" alt="\operatorname{det}\ N" title="\operatorname{det}\ N" data-latex="\operatorname{det}\ N"&gt;?&lt;/li&gt;
    &lt;li&gt;Let &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?Q" alt="Q" title="Q" data-latex="Q"&gt; be the matrix obtained from &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"&gt; by applying the row operation &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_1%20%5Cleftrightarrow%20R_2" alt="R_1 \leftrightarrow R_2" title="R_1 \leftrightarrow R_2" data-latex="R_1 \leftrightarrow R_2"&gt;. What is &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Coperatorname%7Bdet%7D%5C%20Q" alt="\operatorname{det}\ Q" title="\operatorname{det}\ Q" data-latex="\operatorname{det}\ Q"&gt;?&lt;/li&gt;
    &lt;li&gt;Let &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?C" alt="C" title="C" data-latex="C"&gt; be the matrix obtained from &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A" alt="A" title="A" data-latex="A"&gt; by applying the row operation &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?R_1%20%5Cto%20R_1%20+%205R_2" alt="R_1 \to R_1 + 5R_2" title="R_1 \to R_1 + 5R_2" data-latex="R_1 \to R_1 + 5R_2"&gt;. What is &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Coperatorname%7Bdet%7D%5C%20C" alt="\operatorname{det}\ C" title="\operatorname{det}\ C" data-latex="\operatorname{det}\ C"&gt;?&lt;/li&gt;
  &lt;/ol&gt;
&lt;/div&gt;

</mattext>
    </material>
    <response_str ident="response1" rcardinality="Single">
      <render_fib>
        <response_label ident="answer1" rshuffle="No"/>
      </render_fib>
    </response_str>
  </presentation>
  <itemfeedback ident="general_fb">
    <flow_mat>
      <material>
        <mattextxml>
          <div class="exercise-answer">
            <h4>Partial Answer:</h4>
            <ol type="a">
              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ N= -18" alt="\operatorname{det}\ N= -18" title="\operatorname{det}\ N= -18" data-latex="\operatorname{det}\ N= -18"/>
              </li>
              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ Q= -6" alt="\operatorname{det}\ Q= -6" title="\operatorname{det}\ Q= -6" data-latex="\operatorname{det}\ Q= -6"/>
              </li>
              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ C= 6" alt="\operatorname{det}\ C= 6" title="\operatorname{det}\ C= 6" data-latex="\operatorname{det}\ C= 6"/>
              </li>
            </ol>
          </div>
        </mattextxml>
        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;ol type="a"&gt;
    &lt;li&gt;
      &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Coperatorname%7Bdet%7D%5C%20N=%20-18" alt="\operatorname{det}\ N= -18" title="\operatorname{det}\ N= -18" data-latex="\operatorname{det}\ N= -18"&gt;
    &lt;/li&gt;
    &lt;li&gt;
      &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Coperatorname%7Bdet%7D%5C%20Q=%20-6" alt="\operatorname{det}\ Q= -6" title="\operatorname{det}\ Q= -6" data-latex="\operatorname{det}\ Q= -6"&gt;
    &lt;/li&gt;
    &lt;li&gt;
      &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Coperatorname%7Bdet%7D%5C%20C=%206" alt="\operatorname{det}\ C= 6" title="\operatorname{det}\ C= 6" data-latex="\operatorname{det}\ C= 6"&gt;
    &lt;/li&gt;
  &lt;/ol&gt;
&lt;/div&gt;

</mattext>
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  </itemfeedback>
</item>