0010.qti

<item ident="M3-0010" title="M3 | Invertible matrices | ver. 0010">
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  <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?Q= \left[\begin{array}{cccc} -3 &amp; -3 &amp; 1 &amp; 1 \\ 4 &amp; 5 &amp; -2 &amp; -2 \\ -4 &amp; -4 &amp; 1 &amp; 3 \\ -3 &amp; -3 &amp; 0 &amp; 7 \end{array}\right]" alt="Q= \left[\begin{array}{cccc} -3 &amp; -3 &amp; 1 &amp; 1 \\ 4 &amp; 5 &amp; -2 &amp; -2 \\ -4 &amp; -4 &amp; 1 &amp; 3 \\ -3 &amp; -3 &amp; 0 &amp; 7 \end{array}\right]" title="Q= \left[\begin{array}{cccc} -3 &amp; -3 &amp; 1 &amp; 1 \\ 4 &amp; 5 &amp; -2 &amp; -2 \\ -4 &amp; -4 &amp; 1 &amp; 3 \\ -3 &amp; -3 &amp; 0 &amp; 7 \end{array}\right]" data-latex="Q= \left[\begin{array}{cccc} -3 &amp; -3 &amp; 1 &amp; 1 \\ 4 &amp; 5 &amp; -2 &amp; -2 \\ -4 &amp; -4 &amp; 1 &amp; 3 \\ -3 &amp; -3 &amp; 0 &amp; 7 \end{array}\right]"/> is or is not invertible.</p>
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      <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?Q=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%20-3%20&amp;amp;%20-3%20&amp;amp;%201%20&amp;amp;%201%20%5C%5C%204%20&amp;amp;%205%20&amp;amp;%20-2%20&amp;amp;%20-2%20%5C%5C%20-4%20&amp;amp;%20-4%20&amp;amp;%201%20&amp;amp;%203%20%5C%5C%20-3%20&amp;amp;%20-3%20&amp;amp;%200%20&amp;amp;%207%20%5Cend%7Barray%7D%5Cright%5D" alt="Q= \left[\begin{array}{cccc} -3 &amp;amp; -3 &amp;amp; 1 &amp;amp; 1 \\ 4 &amp;amp; 5 &amp;amp; -2 &amp;amp; -2 \\ -4 &amp;amp; -4 &amp;amp; 1 &amp;amp; 3 \\ -3 &amp;amp; -3 &amp;amp; 0 &amp;amp; 7 \end{array}\right]" title="Q= \left[\begin{array}{cccc} -3 &amp;amp; -3 &amp;amp; 1 &amp;amp; 1 \\ 4 &amp;amp; 5 &amp;amp; -2 &amp;amp; -2 \\ -4 &amp;amp; -4 &amp;amp; 1 &amp;amp; 3 \\ -3 &amp;amp; -3 &amp;amp; 0 &amp;amp; 7 \end{array}\right]" data-latex="Q= \left[\begin{array}{cccc} -3 &amp;amp; -3 &amp;amp; 1 &amp;amp; 1 \\ 4 &amp;amp; 5 &amp;amp; -2 &amp;amp; -2 \\ -4 &amp;amp; -4 &amp;amp; 1 &amp;amp; 3 \\ -3 &amp;amp; -3 &amp;amp; 0 &amp;amp; 7 \end{array}\right]"&gt; is or is not invertible.&lt;/p&gt;
&lt;/div&gt;

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  <itemfeedback ident="general_fb">
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          <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} -3 &amp; -3 &amp; 1 &amp; 1 \\ 4 &amp; 5 &amp; -2 &amp; -2 \\ -4 &amp; -4 &amp; 1 &amp; 3 \\ -3 &amp; -3 &amp; 0 &amp; 7 \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} -3 &amp; -3 &amp; 1 &amp; 1 \\ 4 &amp; 5 &amp; -2 &amp; -2 \\ -4 &amp; -4 &amp; 1 &amp; 3 \\ -3 &amp; -3 &amp; 0 &amp; 7 \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} -3 &amp; -3 &amp; 1 &amp; 1 \\ 4 &amp; 5 &amp; -2 &amp; -2 \\ -4 &amp; -4 &amp; 1 &amp; 3 \\ -3 &amp; -3 &amp; 0 &amp; 7 \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} -3 &amp; -3 &amp; 1 &amp; 1 \\ 4 &amp; 5 &amp; -2 &amp; -2 \\ -4 &amp; -4 &amp; 1 &amp; 3 \\ -3 &amp; -3 &amp; 0 &amp; 7 \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?Q" alt="Q" title="Q" data-latex="Q"/> 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%20-3%20&amp;amp;%20-3%20&amp;amp;%201%20&amp;amp;%201%20%5C%5C%204%20&amp;amp;%205%20&amp;amp;%20-2%20&amp;amp;%20-2%20%5C%5C%20-4%20&amp;amp;%20-4%20&amp;amp;%201%20&amp;amp;%203%20%5C%5C%20-3%20&amp;amp;%20-3%20&amp;amp;%200%20&amp;amp;%207%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} -3 &amp;amp; -3 &amp;amp; 1 &amp;amp; 1 \\ 4 &amp;amp; 5 &amp;amp; -2 &amp;amp; -2 \\ -4 &amp;amp; -4 &amp;amp; 1 &amp;amp; 3 \\ -3 &amp;amp; -3 &amp;amp; 0 &amp;amp; 7 \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} -3 &amp;amp; -3 &amp;amp; 1 &amp;amp; 1 \\ 4 &amp;amp; 5 &amp;amp; -2 &amp;amp; -2 \\ -4 &amp;amp; -4 &amp;amp; 1 &amp;amp; 3 \\ -3 &amp;amp; -3 &amp;amp; 0 &amp;amp; 7 \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} -3 &amp;amp; -3 &amp;amp; 1 &amp;amp; 1 \\ 4 &amp;amp; 5 &amp;amp; -2 &amp;amp; -2 \\ -4 &amp;amp; -4 &amp;amp; 1 &amp;amp; 3 \\ -3 &amp;amp; -3 &amp;amp; 0 &amp;amp; 7 \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?Q" alt="Q" title="Q" data-latex="Q"&gt; is invertible.&lt;/div&gt;

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