0005.qti

<item ident="M1-0005" title="M1 | Multiplying matrices | ver. 0005">
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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} 0 &amp; -1 &amp; -2 \\ -2 &amp; -5 &amp; 2 \\ 1 &amp; 0 &amp; 0 \\ -1 &amp; -4 &amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} -1 &amp; -5 \\ 2 &amp; -5 \\ 1 &amp; 1 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 &amp; 2 \\ -2 &amp; -3 \\ -3 &amp; -1 \\ 5 &amp; 6 \end{array}\right]" alt="A= \left[\begin{array}{ccc} 0 &amp; -1 &amp; -2 \\ -2 &amp; -5 &amp; 2 \\ 1 &amp; 0 &amp; 0 \\ -1 &amp; -4 &amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} -1 &amp; -5 \\ 2 &amp; -5 \\ 1 &amp; 1 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 &amp; 2 \\ -2 &amp; -3 \\ -3 &amp; -1 \\ 5 &amp; 6 \end{array}\right]" title="A= \left[\begin{array}{ccc} 0 &amp; -1 &amp; -2 \\ -2 &amp; -5 &amp; 2 \\ 1 &amp; 0 &amp; 0 \\ -1 &amp; -4 &amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} -1 &amp; -5 \\ 2 &amp; -5 \\ 1 &amp; 1 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 &amp; 2 \\ -2 &amp; -3 \\ -3 &amp; -1 \\ 5 &amp; 6 \end{array}\right]" data-latex="A= \left[\begin{array}{ccc} 0 &amp; -1 &amp; -2 \\ -2 &amp; -5 &amp; 2 \\ 1 &amp; 0 &amp; 0 \\ -1 &amp; -4 &amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} -1 &amp; -5 \\ 2 &amp; -5 \\ 1 &amp; 1 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 &amp; 2 \\ -2 &amp; -3 \\ -3 &amp; -1 \\ 5 &amp; 6 \end{array}\right]"/></p> Explain which two can be multiplied and why. Then show how to find their product.</p>
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      <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%200%20&amp;amp;%20-1%20&amp;amp;%20-2%20%5C%5C%20-2%20&amp;amp;%20-5%20&amp;amp;%202%20%5C%5C%201%20&amp;amp;%200%20&amp;amp;%200%20%5C%5C%20-1%20&amp;amp;%20-4%20&amp;amp;%20-1%20%5Cend%7Barray%7D%5Cright%5D%20%5Chspace%7B1em%7D%20B=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20-1%20&amp;amp;%20-5%20%5C%5C%202%20&amp;amp;%20-5%20%5C%5C%201%20&amp;amp;%201%20%5Cend%7Barray%7D%5Cright%5D%20%5Chspace%7B1em%7D%20C=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%201%20&amp;amp;%202%20%5C%5C%20-2%20&amp;amp;%20-3%20%5C%5C%20-3%20&amp;amp;%20-1%20%5C%5C%205%20&amp;amp;%206%20%5Cend%7Barray%7D%5Cright%5D" alt="A= \left[\begin{array}{ccc} 0 &amp;amp; -1 &amp;amp; -2 \\ -2 &amp;amp; -5 &amp;amp; 2 \\ 1 &amp;amp; 0 &amp;amp; 0 \\ -1 &amp;amp; -4 &amp;amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} -1 &amp;amp; -5 \\ 2 &amp;amp; -5 \\ 1 &amp;amp; 1 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 &amp;amp; 2 \\ -2 &amp;amp; -3 \\ -3 &amp;amp; -1 \\ 5 &amp;amp; 6 \end{array}\right]" title="A= \left[\begin{array}{ccc} 0 &amp;amp; -1 &amp;amp; -2 \\ -2 &amp;amp; -5 &amp;amp; 2 \\ 1 &amp;amp; 0 &amp;amp; 0 \\ -1 &amp;amp; -4 &amp;amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} -1 &amp;amp; -5 \\ 2 &amp;amp; -5 \\ 1 &amp;amp; 1 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 &amp;amp; 2 \\ -2 &amp;amp; -3 \\ -3 &amp;amp; -1 \\ 5 &amp;amp; 6 \end{array}\right]" data-latex="A= \left[\begin{array}{ccc} 0 &amp;amp; -1 &amp;amp; -2 \\ -2 &amp;amp; -5 &amp;amp; 2 \\ 1 &amp;amp; 0 &amp;amp; 0 \\ -1 &amp;amp; -4 &amp;amp; -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} -1 &amp;amp; -5 \\ 2 &amp;amp; -5 \\ 1 &amp;amp; 1 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 &amp;amp; 2 \\ -2 &amp;amp; -3 \\ -3 &amp;amp; -1 \\ 5 &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;

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    <response_str ident="response1" rcardinality="Single">
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        <response_label ident="answer1" rshuffle="No"/>
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  </presentation>
  <itemfeedback ident="general_fb">
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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?AB= \left[\begin{array}{cc} -4 &amp; 3 \\ -6 &amp; 37 \\ -1 &amp; -5 \\ -8 &amp; 24 \end{array}\right]" alt="AB= \left[\begin{array}{cc} -4 &amp; 3 \\ -6 &amp; 37 \\ -1 &amp; -5 \\ -8 &amp; 24 \end{array}\right]" title="AB= \left[\begin{array}{cc} -4 &amp; 3 \\ -6 &amp; 37 \\ -1 &amp; -5 \\ -8 &amp; 24 \end{array}\right]" data-latex="AB= \left[\begin{array}{cc} -4 &amp; 3 \\ -6 &amp; 37 \\ -1 &amp; -5 \\ -8 &amp; 24 \end{array}\right]"/>
            </p>
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        <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?AB=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20-4%20&amp;amp;%203%20%5C%5C%20-6%20&amp;amp;%2037%20%5C%5C%20-1%20&amp;amp;%20-5%20%5C%5C%20-8%20&amp;amp;%2024%20%5Cend%7Barray%7D%5Cright%5D" alt="AB= \left[\begin{array}{cc} -4 &amp;amp; 3 \\ -6 &amp;amp; 37 \\ -1 &amp;amp; -5 \\ -8 &amp;amp; 24 \end{array}\right]" title="AB= \left[\begin{array}{cc} -4 &amp;amp; 3 \\ -6 &amp;amp; 37 \\ -1 &amp;amp; -5 \\ -8 &amp;amp; 24 \end{array}\right]" data-latex="AB= \left[\begin{array}{cc} -4 &amp;amp; 3 \\ -6 &amp;amp; 37 \\ -1 &amp;amp; -5 \\ -8 &amp;amp; 24 \end{array}\right]"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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