0010.qti

<item ident="M4-0010" title="M4 | Finding a matrix inverse | ver. 0010">
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  <presentation>
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          <p>
            <strong>M4.</strong>
          </p>
          <p>Show how to find the inverse of the matrix <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A= \left[\begin{array}{cccc} 1 &amp; -1 &amp; 3 &amp; 5 \\ 0 &amp; 1 &amp; -5 &amp; -8 \\ 0 &amp; 0 &amp; 1 &amp; 2 \\ 0 &amp; 1 &amp; -3 &amp; -3 \end{array}\right]" alt="A= \left[\begin{array}{cccc} 1 &amp; -1 &amp; 3 &amp; 5 \\ 0 &amp; 1 &amp; -5 &amp; -8 \\ 0 &amp; 0 &amp; 1 &amp; 2 \\ 0 &amp; 1 &amp; -3 &amp; -3 \end{array}\right]" title="A= \left[\begin{array}{cccc} 1 &amp; -1 &amp; 3 &amp; 5 \\ 0 &amp; 1 &amp; -5 &amp; -8 \\ 0 &amp; 0 &amp; 1 &amp; 2 \\ 0 &amp; 1 &amp; -3 &amp; -3 \end{array}\right]" data-latex="A= \left[\begin{array}{cccc} 1 &amp; -1 &amp; 3 &amp; 5 \\ 0 &amp; 1 &amp; -5 &amp; -8 \\ 0 &amp; 0 &amp; 1 &amp; 2 \\ 0 &amp; 1 &amp; -3 &amp; -3 \end{array}\right]"/>.</p>
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      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;M4.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Show how to find the inverse of the matrix &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%7Bcccc%7D%201%20&amp;amp;%20-1%20&amp;amp;%203%20&amp;amp;%205%20%5C%5C%200%20&amp;amp;%201%20&amp;amp;%20-5%20&amp;amp;%20-8%20%5C%5C%200%20&amp;amp;%200%20&amp;amp;%201%20&amp;amp;%202%20%5C%5C%200%20&amp;amp;%201%20&amp;amp;%20-3%20&amp;amp;%20-3%20%5Cend%7Barray%7D%5Cright%5D" alt="A= \left[\begin{array}{cccc} 1 &amp;amp; -1 &amp;amp; 3 &amp;amp; 5 \\ 0 &amp;amp; 1 &amp;amp; -5 &amp;amp; -8 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 2 \\ 0 &amp;amp; 1 &amp;amp; -3 &amp;amp; -3 \end{array}\right]" title="A= \left[\begin{array}{cccc} 1 &amp;amp; -1 &amp;amp; 3 &amp;amp; 5 \\ 0 &amp;amp; 1 &amp;amp; -5 &amp;amp; -8 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 2 \\ 0 &amp;amp; 1 &amp;amp; -3 &amp;amp; -3 \end{array}\right]" data-latex="A= \left[\begin{array}{cccc} 1 &amp;amp; -1 &amp;amp; 3 &amp;amp; 5 \\ 0 &amp;amp; 1 &amp;amp; -5 &amp;amp; -8 \\ 0 &amp;amp; 0 &amp;amp; 1 &amp;amp; 2 \\ 0 &amp;amp; 1 &amp;amp; -3 &amp;amp; -3 \end{array}\right]"&gt;.&lt;/p&gt;
&lt;/div&gt;

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            <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?A^{-1}= \left[\begin{array}{cccc} 1 &amp; 2 &amp; 4 &amp; -1 \\ 0 &amp; 3 &amp; 9 &amp; -2 \\ 0 &amp; 2 &amp; 5 &amp; -2 \\ 0 &amp; -1 &amp; -2 &amp; 1 \end{array}\right]" alt="A^{-1}= \left[\begin{array}{cccc} 1 &amp; 2 &amp; 4 &amp; -1 \\ 0 &amp; 3 &amp; 9 &amp; -2 \\ 0 &amp; 2 &amp; 5 &amp; -2 \\ 0 &amp; -1 &amp; -2 &amp; 1 \end{array}\right]" title="A^{-1}= \left[\begin{array}{cccc} 1 &amp; 2 &amp; 4 &amp; -1 \\ 0 &amp; 3 &amp; 9 &amp; -2 \\ 0 &amp; 2 &amp; 5 &amp; -2 \\ 0 &amp; -1 &amp; -2 &amp; 1 \end{array}\right]" data-latex="A^{-1}= \left[\begin{array}{cccc} 1 &amp; 2 &amp; 4 &amp; -1 \\ 0 &amp; 3 &amp; 9 &amp; -2 \\ 0 &amp; 2 &amp; 5 &amp; -2 \\ 0 &amp; -1 &amp; -2 &amp; 1 \end{array}\right]"/>
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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?A%5E%7B-1%7D=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%201%20&amp;amp;%202%20&amp;amp;%204%20&amp;amp;%20-1%20%5C%5C%200%20&amp;amp;%203%20&amp;amp;%209%20&amp;amp;%20-2%20%5C%5C%200%20&amp;amp;%202%20&amp;amp;%205%20&amp;amp;%20-2%20%5C%5C%200%20&amp;amp;%20-1%20&amp;amp;%20-2%20&amp;amp;%201%20%5Cend%7Barray%7D%5Cright%5D" alt="A^{-1}= \left[\begin{array}{cccc} 1 &amp;amp; 2 &amp;amp; 4 &amp;amp; -1 \\ 0 &amp;amp; 3 &amp;amp; 9 &amp;amp; -2 \\ 0 &amp;amp; 2 &amp;amp; 5 &amp;amp; -2 \\ 0 &amp;amp; -1 &amp;amp; -2 &amp;amp; 1 \end{array}\right]" title="A^{-1}= \left[\begin{array}{cccc} 1 &amp;amp; 2 &amp;amp; 4 &amp;amp; -1 \\ 0 &amp;amp; 3 &amp;amp; 9 &amp;amp; -2 \\ 0 &amp;amp; 2 &amp;amp; 5 &amp;amp; -2 \\ 0 &amp;amp; -1 &amp;amp; -2 &amp;amp; 1 \end{array}\right]" data-latex="A^{-1}= \left[\begin{array}{cccc} 1 &amp;amp; 2 &amp;amp; 4 &amp;amp; -1 \\ 0 &amp;amp; 3 &amp;amp; 9 &amp;amp; -2 \\ 0 &amp;amp; 2 &amp;amp; 5 &amp;amp; -2 \\ 0 &amp;amp; -1 &amp;amp; -2 &amp;amp; 1 \end{array}\right]"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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