0004.qti

<item ident="M1-0004" title="M1 | Multiplying 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>M1.</strong>
          </p>
          <p>Of the following three matrices, only two may be multiplied. <p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A= \left[\begin{array}{ccc} 2 &amp; -1 &amp; -1 \\ 1 &amp; 0 &amp; -2 \\ 3 &amp; -1 &amp; -2 \\ 2 &amp; -1 &amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} 3 &amp; 3 \\ 0 &amp; 1 \\ -2 &amp; -2 \\ 1 &amp; 0 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 3 &amp; 5 &amp; -3 \\ 1 &amp; 2 &amp; -1 \end{array}\right]" alt="A= \left[\begin{array}{ccc} 2 &amp; -1 &amp; -1 \\ 1 &amp; 0 &amp; -2 \\ 3 &amp; -1 &amp; -2 \\ 2 &amp; -1 &amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} 3 &amp; 3 \\ 0 &amp; 1 \\ -2 &amp; -2 \\ 1 &amp; 0 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 3 &amp; 5 &amp; -3 \\ 1 &amp; 2 &amp; -1 \end{array}\right]" title="A= \left[\begin{array}{ccc} 2 &amp; -1 &amp; -1 \\ 1 &amp; 0 &amp; -2 \\ 3 &amp; -1 &amp; -2 \\ 2 &amp; -1 &amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} 3 &amp; 3 \\ 0 &amp; 1 \\ -2 &amp; -2 \\ 1 &amp; 0 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 3 &amp; 5 &amp; -3 \\ 1 &amp; 2 &amp; -1 \end{array}\right]" data-latex="A= \left[\begin{array}{ccc} 2 &amp; -1 &amp; -1 \\ 1 &amp; 0 &amp; -2 \\ 3 &amp; -1 &amp; -2 \\ 2 &amp; -1 &amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} 3 &amp; 3 \\ 0 &amp; 1 \\ -2 &amp; -2 \\ 1 &amp; 0 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 3 &amp; 5 &amp; -3 \\ 1 &amp; 2 &amp; -1 \end{array}\right]"/></p> Explain which two can be multiplied and why. Then show how to find their product.</p>
        </div>
      </mattextxml>
      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;M1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Of the following three matrices, only two may be multiplied. &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?A=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%202%20&amp;amp;%20-1%20&amp;amp;%20-1%20%5C%5C%201%20&amp;amp;%200%20&amp;amp;%20-2%20%5C%5C%203%20&amp;amp;%20-1%20&amp;amp;%20-2%20%5C%5C%202%20&amp;amp;%20-1%20&amp;amp;%20-1%20%5Cend%7Barray%7D%5Cright%5D%20%5Chspace%7B1em%7D%20B=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%203%20&amp;amp;%203%20%5C%5C%200%20&amp;amp;%201%20%5C%5C%20-2%20&amp;amp;%20-2%20%5C%5C%201%20&amp;amp;%200%20%5Cend%7Barray%7D%5Cright%5D%20%5Chspace%7B1em%7D%20C=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%203%20&amp;amp;%205%20&amp;amp;%20-3%20%5C%5C%201%20&amp;amp;%202%20&amp;amp;%20-1%20%5Cend%7Barray%7D%5Cright%5D" alt="A= \left[\begin{array}{ccc} 2 &amp;amp; -1 &amp;amp; -1 \\ 1 &amp;amp; 0 &amp;amp; -2 \\ 3 &amp;amp; -1 &amp;amp; -2 \\ 2 &amp;amp; -1 &amp;amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} 3 &amp;amp; 3 \\ 0 &amp;amp; 1 \\ -2 &amp;amp; -2 \\ 1 &amp;amp; 0 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 3 &amp;amp; 5 &amp;amp; -3 \\ 1 &amp;amp; 2 &amp;amp; -1 \end{array}\right]" title="A= \left[\begin{array}{ccc} 2 &amp;amp; -1 &amp;amp; -1 \\ 1 &amp;amp; 0 &amp;amp; -2 \\ 3 &amp;amp; -1 &amp;amp; -2 \\ 2 &amp;amp; -1 &amp;amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} 3 &amp;amp; 3 \\ 0 &amp;amp; 1 \\ -2 &amp;amp; -2 \\ 1 &amp;amp; 0 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 3 &amp;amp; 5 &amp;amp; -3 \\ 1 &amp;amp; 2 &amp;amp; -1 \end{array}\right]" data-latex="A= \left[\begin{array}{ccc} 2 &amp;amp; -1 &amp;amp; -1 \\ 1 &amp;amp; 0 &amp;amp; -2 \\ 3 &amp;amp; -1 &amp;amp; -2 \\ 2 &amp;amp; -1 &amp;amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} 3 &amp;amp; 3 \\ 0 &amp;amp; 1 \\ -2 &amp;amp; -2 \\ 1 &amp;amp; 0 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 3 &amp;amp; 5 &amp;amp; -3 \\ 1 &amp;amp; 2 &amp;amp; -1 \end{array}\right]"&gt;&lt;/p&gt; Explain which two can be multiplied and why. Then show how to find their product.
&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 style="text-align:center;">
              <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?BC= \left[\begin{array}{ccc} 12 &amp; 21 &amp; -12 \\ 1 &amp; 2 &amp; -1 \\ -8 &amp; -14 &amp; 8 \\ 3 &amp; 5 &amp; -3 \end{array}\right]" alt="BC= \left[\begin{array}{ccc} 12 &amp; 21 &amp; -12 \\ 1 &amp; 2 &amp; -1 \\ -8 &amp; -14 &amp; 8 \\ 3 &amp; 5 &amp; -3 \end{array}\right]" title="BC= \left[\begin{array}{ccc} 12 &amp; 21 &amp; -12 \\ 1 &amp; 2 &amp; -1 \\ -8 &amp; -14 &amp; 8 \\ 3 &amp; 5 &amp; -3 \end{array}\right]" data-latex="BC= \left[\begin{array}{ccc} 12 &amp; 21 &amp; -12 \\ 1 &amp; 2 &amp; -1 \\ -8 &amp; -14 &amp; 8 \\ 3 &amp; 5 &amp; -3 \end{array}\right]"/>
            </p>
          </div>
        </mattextxml>
        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&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?BC=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%2012%20&amp;amp;%2021%20&amp;amp;%20-12%20%5C%5C%201%20&amp;amp;%202%20&amp;amp;%20-1%20%5C%5C%20-8%20&amp;amp;%20-14%20&amp;amp;%208%20%5C%5C%203%20&amp;amp;%205%20&amp;amp;%20-3%20%5Cend%7Barray%7D%5Cright%5D" alt="BC= \left[\begin{array}{ccc} 12 &amp;amp; 21 &amp;amp; -12 \\ 1 &amp;amp; 2 &amp;amp; -1 \\ -8 &amp;amp; -14 &amp;amp; 8 \\ 3 &amp;amp; 5 &amp;amp; -3 \end{array}\right]" title="BC= \left[\begin{array}{ccc} 12 &amp;amp; 21 &amp;amp; -12 \\ 1 &amp;amp; 2 &amp;amp; -1 \\ -8 &amp;amp; -14 &amp;amp; 8 \\ 3 &amp;amp; 5 &amp;amp; -3 \end{array}\right]" data-latex="BC= \left[\begin{array}{ccc} 12 &amp;amp; 21 &amp;amp; -12 \\ 1 &amp;amp; 2 &amp;amp; -1 \\ -8 &amp;amp; -14 &amp;amp; 8 \\ 3 &amp;amp; 5 &amp;amp; -3 \end{array}\right]"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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