0004.qti

<item ident="M3-0004" title="M3 | Invertible matrices | ver. 0004">
  <itemmetadata>
    <qtimetadata>
      <qtimetadatafield>
        <fieldlabel>question_type</fieldlabel>
        <fieldentry>essay_question</fieldentry>
      </qtimetadatafield>
    </qtimetadata>
  </itemmetadata>
  <presentation>
    <material>
      <mattextxml>
        <div class="exercise-statement">
          <p>
            <strong>M3.</strong>
          </p>
          <p>Explain why the matrix <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?C= \left[\begin{array}{cccc} 1 &amp; 1 &amp; 3 &amp; -2 \\ 1 &amp; 2 &amp; 6 &amp; -7 \\ -2 &amp; -1 &amp; -2 &amp; -4 \\ -3 &amp; -2 &amp; -8 &amp; 8 \end{array}\right]" alt="C= \left[\begin{array}{cccc} 1 &amp; 1 &amp; 3 &amp; -2 \\ 1 &amp; 2 &amp; 6 &amp; -7 \\ -2 &amp; -1 &amp; -2 &amp; -4 \\ -3 &amp; -2 &amp; -8 &amp; 8 \end{array}\right]" title="C= \left[\begin{array}{cccc} 1 &amp; 1 &amp; 3 &amp; -2 \\ 1 &amp; 2 &amp; 6 &amp; -7 \\ -2 &amp; -1 &amp; -2 &amp; -4 \\ -3 &amp; -2 &amp; -8 &amp; 8 \end{array}\right]" data-latex="C= \left[\begin{array}{cccc} 1 &amp; 1 &amp; 3 &amp; -2 \\ 1 &amp; 2 &amp; 6 &amp; -7 \\ -2 &amp; -1 &amp; -2 &amp; -4 \\ -3 &amp; -2 &amp; -8 &amp; 8 \end{array}\right]"/> is or is not invertible.</p>
        </div>
      </mattextxml>
      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;M3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Explain why the matrix &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?C=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%201%20&amp;amp;%201%20&amp;amp;%203%20&amp;amp;%20-2%20%5C%5C%201%20&amp;amp;%202%20&amp;amp;%206%20&amp;amp;%20-7%20%5C%5C%20-2%20&amp;amp;%20-1%20&amp;amp;%20-2%20&amp;amp;%20-4%20%5C%5C%20-3%20&amp;amp;%20-2%20&amp;amp;%20-8%20&amp;amp;%208%20%5Cend%7Barray%7D%5Cright%5D" alt="C= \left[\begin{array}{cccc} 1 &amp;amp; 1 &amp;amp; 3 &amp;amp; -2 \\ 1 &amp;amp; 2 &amp;amp; 6 &amp;amp; -7 \\ -2 &amp;amp; -1 &amp;amp; -2 &amp;amp; -4 \\ -3 &amp;amp; -2 &amp;amp; -8 &amp;amp; 8 \end{array}\right]" title="C= \left[\begin{array}{cccc} 1 &amp;amp; 1 &amp;amp; 3 &amp;amp; -2 \\ 1 &amp;amp; 2 &amp;amp; 6 &amp;amp; -7 \\ -2 &amp;amp; -1 &amp;amp; -2 &amp;amp; -4 \\ -3 &amp;amp; -2 &amp;amp; -8 &amp;amp; 8 \end{array}\right]" data-latex="C= \left[\begin{array}{cccc} 1 &amp;amp; 1 &amp;amp; 3 &amp;amp; -2 \\ 1 &amp;amp; 2 &amp;amp; 6 &amp;amp; -7 \\ -2 &amp;amp; -1 &amp;amp; -2 &amp;amp; -4 \\ -3 &amp;amp; -2 &amp;amp; -8 &amp;amp; 8 \end{array}\right]"&gt; is or is not invertible.&lt;/p&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><p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{RREF} \left[\begin{array}{cccc} 1 &amp; 1 &amp; 3 &amp; -2 \\ 1 &amp; 2 &amp; 6 &amp; -7 \\ -2 &amp; -1 &amp; -2 &amp; -4 \\ -3 &amp; -2 &amp; -8 &amp; 8 \end{array}\right] = \left[\begin{array}{cccc} 1 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" alt="\operatorname{RREF} \left[\begin{array}{cccc} 1 &amp; 1 &amp; 3 &amp; -2 \\ 1 &amp; 2 &amp; 6 &amp; -7 \\ -2 &amp; -1 &amp; -2 &amp; -4 \\ -3 &amp; -2 &amp; -8 &amp; 8 \end{array}\right] = \left[\begin{array}{cccc} 1 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" title="\operatorname{RREF} \left[\begin{array}{cccc} 1 &amp; 1 &amp; 3 &amp; -2 \\ 1 &amp; 2 &amp; 6 &amp; -7 \\ -2 &amp; -1 &amp; -2 &amp; -4 \\ -3 &amp; -2 &amp; -8 &amp; 8 \end{array}\right] = \left[\begin{array}{cccc} 1 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]" data-latex="\operatorname{RREF} \left[\begin{array}{cccc} 1 &amp; 1 &amp; 3 &amp; -2 \\ 1 &amp; 2 &amp; 6 &amp; -7 \\ -2 &amp; -1 &amp; -2 &amp; -4 \\ -3 &amp; -2 &amp; -8 &amp; 8 \end{array}\right] = \left[\begin{array}{cccc} 1 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; 1 \end{array}\right]"/></p></p><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"/> is invertible.</div>
        </mattextxml>
        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
&lt;h4&gt;Partial Answer:&lt;/h4&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p style="text-align:center;"&gt;&lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Coperatorname%7BRREF%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%201%20&amp;amp;%201%20&amp;amp;%203%20&amp;amp;%20-2%20%5C%5C%201%20&amp;amp;%202%20&amp;amp;%206%20&amp;amp;%20-7%20%5C%5C%20-2%20&amp;amp;%20-1%20&amp;amp;%20-2%20&amp;amp;%20-4%20%5C%5C%20-3%20&amp;amp;%20-2%20&amp;amp;%20-8%20&amp;amp;%208%20%5Cend%7Barray%7D%5Cright%5D%20=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%201%20&amp;amp;%200%20&amp;amp;%200%20&amp;amp;%200%20%5C%5C%200%20&amp;amp;%201%20&amp;amp;%200%20&amp;amp;%200%20%5C%5C%200%20&amp;amp;%200%20&amp;amp;%201%20&amp;amp;%200%20%5C%5C%200%20&amp;amp;%200%20&amp;amp;%200%20&amp;amp;%201%20%5Cend%7Barray%7D%5Cright%5D" alt="\operatorname{RREF} \left[\begin{array}{cccc} 1 &amp;amp; 1 &amp;amp; 3 &amp;amp; -2 \\ 1 &amp;amp; 2 &amp;amp; 6 &amp;amp; -7 \\ -2 &amp;amp; -1 &amp;amp; -2 &amp;amp; -4 \\ -3 &amp;amp; -2 &amp;amp; -8 &amp;amp; 8 \end{array}\right] = \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" title="\operatorname{RREF} \left[\begin{array}{cccc} 1 &amp;amp; 1 &amp;amp; 3 &amp;amp; -2 \\ 1 &amp;amp; 2 &amp;amp; 6 &amp;amp; -7 \\ -2 &amp;amp; -1 &amp;amp; -2 &amp;amp; -4 \\ -3 &amp;amp; -2 &amp;amp; -8 &amp;amp; 8 \end{array}\right] = \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]" data-latex="\operatorname{RREF} \left[\begin{array}{cccc} 1 &amp;amp; 1 &amp;amp; 3 &amp;amp; -2 \\ 1 &amp;amp; 2 &amp;amp; 6 &amp;amp; -7 \\ -2 &amp;amp; -1 &amp;amp; -2 &amp;amp; -4 \\ -3 &amp;amp; -2 &amp;amp; -8 &amp;amp; 8 \end{array}\right] = \left[\begin{array}{cccc} 1 &amp;amp; 0 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 1 &amp;amp; 0 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 0 \\ 0 &amp;amp; 0 &amp;amp; 0 &amp;amp; 1 \end{array}\right]"&gt;&lt;/p&gt;
&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; is invertible.&lt;/div&gt;

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