0009.qti

<item ident="M1-0009" title="M1 | Multiplying matrices | ver. 0009">
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  <presentation>
    <material>
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        <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} 1 &amp; -1 &amp; -2 \\ 3 &amp; -2 &amp; -3 \\ -5 &amp; 3 &amp; 5 \\ 0 &amp; 2 &amp; 4 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} -1 &amp; -5 &amp; -2 \\ 1 &amp; 4 &amp; 2 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} -3 &amp; 4 \\ 0 &amp; 1 \\ 3 &amp; -1 \\ 4 &amp; -6 \end{array}\right]" alt="A= \left[\begin{array}{ccc} 1 &amp; -1 &amp; -2 \\ 3 &amp; -2 &amp; -3 \\ -5 &amp; 3 &amp; 5 \\ 0 &amp; 2 &amp; 4 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} -1 &amp; -5 &amp; -2 \\ 1 &amp; 4 &amp; 2 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} -3 &amp; 4 \\ 0 &amp; 1 \\ 3 &amp; -1 \\ 4 &amp; -6 \end{array}\right]" title="A= \left[\begin{array}{ccc} 1 &amp; -1 &amp; -2 \\ 3 &amp; -2 &amp; -3 \\ -5 &amp; 3 &amp; 5 \\ 0 &amp; 2 &amp; 4 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} -1 &amp; -5 &amp; -2 \\ 1 &amp; 4 &amp; 2 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} -3 &amp; 4 \\ 0 &amp; 1 \\ 3 &amp; -1 \\ 4 &amp; -6 \end{array}\right]" data-latex="A= \left[\begin{array}{ccc} 1 &amp; -1 &amp; -2 \\ 3 &amp; -2 &amp; -3 \\ -5 &amp; 3 &amp; 5 \\ 0 &amp; 2 &amp; 4 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} -1 &amp; -5 &amp; -2 \\ 1 &amp; 4 &amp; 2 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} -3 &amp; 4 \\ 0 &amp; 1 \\ 3 &amp; -1 \\ 4 &amp; -6 \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%201%20&amp;amp;%20-1%20&amp;amp;%20-2%20%5C%5C%203%20&amp;amp;%20-2%20&amp;amp;%20-3%20%5C%5C%20-5%20&amp;amp;%203%20&amp;amp;%205%20%5C%5C%200%20&amp;amp;%202%20&amp;amp;%204%20%5Cend%7Barray%7D%5Cright%5D%20%5Chspace%7B1em%7D%20B=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20-1%20&amp;amp;%20-5%20&amp;amp;%20-2%20%5C%5C%201%20&amp;amp;%204%20&amp;amp;%202%20%5Cend%7Barray%7D%5Cright%5D%20%5Chspace%7B1em%7D%20C=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20-3%20&amp;amp;%204%20%5C%5C%200%20&amp;amp;%201%20%5C%5C%203%20&amp;amp;%20-1%20%5C%5C%204%20&amp;amp;%20-6%20%5Cend%7Barray%7D%5Cright%5D" alt="A= \left[\begin{array}{ccc} 1 &amp;amp; -1 &amp;amp; -2 \\ 3 &amp;amp; -2 &amp;amp; -3 \\ -5 &amp;amp; 3 &amp;amp; 5 \\ 0 &amp;amp; 2 &amp;amp; 4 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} -1 &amp;amp; -5 &amp;amp; -2 \\ 1 &amp;amp; 4 &amp;amp; 2 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} -3 &amp;amp; 4 \\ 0 &amp;amp; 1 \\ 3 &amp;amp; -1 \\ 4 &amp;amp; -6 \end{array}\right]" title="A= \left[\begin{array}{ccc} 1 &amp;amp; -1 &amp;amp; -2 \\ 3 &amp;amp; -2 &amp;amp; -3 \\ -5 &amp;amp; 3 &amp;amp; 5 \\ 0 &amp;amp; 2 &amp;amp; 4 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} -1 &amp;amp; -5 &amp;amp; -2 \\ 1 &amp;amp; 4 &amp;amp; 2 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} -3 &amp;amp; 4 \\ 0 &amp;amp; 1 \\ 3 &amp;amp; -1 \\ 4 &amp;amp; -6 \end{array}\right]" data-latex="A= \left[\begin{array}{ccc} 1 &amp;amp; -1 &amp;amp; -2 \\ 3 &amp;amp; -2 &amp;amp; -3 \\ -5 &amp;amp; 3 &amp;amp; 5 \\ 0 &amp;amp; 2 &amp;amp; 4 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} -1 &amp;amp; -5 &amp;amp; -2 \\ 1 &amp;amp; 4 &amp;amp; 2 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} -3 &amp;amp; 4 \\ 0 &amp;amp; 1 \\ 3 &amp;amp; -1 \\ 4 &amp;amp; -6 \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"/>
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  </presentation>
  <itemfeedback ident="general_fb">
    <flow_mat>
      <material>
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          <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?CB= \left[\begin{array}{ccc} 7 &amp; 31 &amp; 14 \\ 1 &amp; 4 &amp; 2 \\ -4 &amp; -19 &amp; -8 \\ -10 &amp; -44 &amp; -20 \end{array}\right]" alt="CB= \left[\begin{array}{ccc} 7 &amp; 31 &amp; 14 \\ 1 &amp; 4 &amp; 2 \\ -4 &amp; -19 &amp; -8 \\ -10 &amp; -44 &amp; -20 \end{array}\right]" title="CB= \left[\begin{array}{ccc} 7 &amp; 31 &amp; 14 \\ 1 &amp; 4 &amp; 2 \\ -4 &amp; -19 &amp; -8 \\ -10 &amp; -44 &amp; -20 \end{array}\right]" data-latex="CB= \left[\begin{array}{ccc} 7 &amp; 31 &amp; 14 \\ 1 &amp; 4 &amp; 2 \\ -4 &amp; -19 &amp; -8 \\ -10 &amp; -44 &amp; -20 \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?CB=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%207%20&amp;amp;%2031%20&amp;amp;%2014%20%5C%5C%201%20&amp;amp;%204%20&amp;amp;%202%20%5C%5C%20-4%20&amp;amp;%20-19%20&amp;amp;%20-8%20%5C%5C%20-10%20&amp;amp;%20-44%20&amp;amp;%20-20%20%5Cend%7Barray%7D%5Cright%5D" alt="CB= \left[\begin{array}{ccc} 7 &amp;amp; 31 &amp;amp; 14 \\ 1 &amp;amp; 4 &amp;amp; 2 \\ -4 &amp;amp; -19 &amp;amp; -8 \\ -10 &amp;amp; -44 &amp;amp; -20 \end{array}\right]" title="CB= \left[\begin{array}{ccc} 7 &amp;amp; 31 &amp;amp; 14 \\ 1 &amp;amp; 4 &amp;amp; 2 \\ -4 &amp;amp; -19 &amp;amp; -8 \\ -10 &amp;amp; -44 &amp;amp; -20 \end{array}\right]" data-latex="CB= \left[\begin{array}{ccc} 7 &amp;amp; 31 &amp;amp; 14 \\ 1 &amp;amp; 4 &amp;amp; 2 \\ -4 &amp;amp; -19 &amp;amp; -8 \\ -10 &amp;amp; -44 &amp;amp; -20 \end{array}\right]"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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</item>