0007.qti

<item ident="G1-0007" title="G1 | Row operations and determinants | ver. 0007">
  <itemmetadata>
    <qtimetadata>
      <qtimetadatafield>
        <fieldlabel>question_type</fieldlabel>
        <fieldentry>essay_question</fieldentry>
      </qtimetadatafield>
    </qtimetadata>
  </itemmetadata>
  <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?P" alt="P" title="P" data-latex="P"/> 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_4 \to R_4 + 5R_1" alt="R_4 \to R_4 + 5R_1" title="R_4 \to R_4 + 5R_1" data-latex="R_4 \to R_4 + 5R_1"/>. What is <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ P" alt="\operatorname{det}\ P" title="\operatorname{det}\ P" data-latex="\operatorname{det}\ P"/>?</li>
            <li>Let <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?B" alt="B" title="B" data-latex="B"/> 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_2 \leftrightarrow R_1" alt="R_2 \leftrightarrow R_1" title="R_2 \leftrightarrow R_1" data-latex="R_2 \leftrightarrow R_1"/>. What is <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ B" alt="\operatorname{det}\ B" title="\operatorname{det}\ B" data-latex="\operatorname{det}\ B"/>?</li>
            <li>Let <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?M" alt="M" title="M" data-latex="M"/> 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}\ M" alt="\operatorname{det}\ M" title="\operatorname{det}\ M" data-latex="\operatorname{det}\ M"/>?</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?P" alt="P" title="P" data-latex="P"&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_4%20%5Cto%20R_4%20+%205R_1" alt="R_4 \to R_4 + 5R_1" title="R_4 \to R_4 + 5R_1" data-latex="R_4 \to R_4 + 5R_1"&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%20P" alt="\operatorname{det}\ P" title="\operatorname{det}\ P" data-latex="\operatorname{det}\ P"&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?B" alt="B" title="B" data-latex="B"&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_2%20%5Cleftrightarrow%20R_1" alt="R_2 \leftrightarrow R_1" title="R_2 \leftrightarrow R_1" data-latex="R_2 \leftrightarrow R_1"&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%20B" alt="\operatorname{det}\ B" title="\operatorname{det}\ B" data-latex="\operatorname{det}\ B"&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?M" alt="M" title="M" data-latex="M"&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%203R_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%20M" alt="\operatorname{det}\ M" title="\operatorname{det}\ M" data-latex="\operatorname{det}\ M"&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}\ P= 6" alt="\operatorname{det}\ P= 6" title="\operatorname{det}\ P= 6" data-latex="\operatorname{det}\ P= 6"/>
              </li>
              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ B= -6" alt="\operatorname{det}\ B= -6" title="\operatorname{det}\ B= -6" data-latex="\operatorname{det}\ B= -6"/>
              </li>
              <li>
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ M= 18" alt="\operatorname{det}\ M= 18" title="\operatorname{det}\ M= 18" data-latex="\operatorname{det}\ M= 18"/>
              </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%20P=%206" alt="\operatorname{det}\ P= 6" title="\operatorname{det}\ P= 6" data-latex="\operatorname{det}\ P= 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%20B=%20-6" alt="\operatorname{det}\ B= -6" title="\operatorname{det}\ B= -6" data-latex="\operatorname{det}\ B= -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%20M=%2018" alt="\operatorname{det}\ M= 18" title="\operatorname{det}\ M= 18" data-latex="\operatorname{det}\ M= 18"&gt;
    &lt;/li&gt;
  &lt;/ol&gt;
&lt;/div&gt;

</mattext>
      </material>
    </flow_mat>
  </itemfeedback>
</item>