0005.qti

<item ident="G3-0005" title="G3 | Eigenvalues | ver. 0005">
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        <div class="exercise-statement">
          <p>
            <strong>G3.</strong>
          </p>
          <p>Explain how to find the eigenvalues of the matrix <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" alt="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" title="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" data-latex="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]"/>.</p>
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      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;G3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Explain how to find the eigenvalues of the matrix &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20-4%20&amp;amp;%202%20%5C%5C%208%20&amp;amp;%202%20%5Cend%7Barray%7D%5Cright%5D" alt="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]" title="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]" data-latex="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]"&gt;.&lt;/p&gt;
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            <h4>Partial Answer:</h4>
            <p>The characteristic polynomial of <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" alt="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" title="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" data-latex="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]"/> is <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\lambda^{2} + 2 \lambda - 24" alt="\lambda^{2} + 2 \lambda - 24" title="\lambda^{2} + 2 \lambda - 24" data-latex="\lambda^{2} + 2 \lambda - 24"/>.</p>
            <p>The eigenvalues of <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" alt="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" title="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]" data-latex="\left[\begin{array}{cc} -4 &amp; 2 \\ 8 &amp; 2 \end{array}\right]"/> are <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-6" alt="-6" title="-6" data-latex="-6"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4" alt="4" title="4" data-latex="4"/>.</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&gt;The characteristic polynomial of &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20-4%20&amp;amp;%202%20%5C%5C%208%20&amp;amp;%202%20%5Cend%7Barray%7D%5Cright%5D" alt="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]" title="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]" data-latex="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]"&gt; is &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Clambda%5E%7B2%7D%20+%202%20%5Clambda%20-%2024" alt="\lambda^{2} + 2 \lambda - 24" title="\lambda^{2} + 2 \lambda - 24" data-latex="\lambda^{2} + 2 \lambda - 24"&gt;.&lt;/p&gt;
  &lt;p&gt;The eigenvalues of &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20-4%20&amp;amp;%202%20%5C%5C%208%20&amp;amp;%202%20%5Cend%7Barray%7D%5Cright%5D" alt="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]" title="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]" data-latex="\left[\begin{array}{cc} -4 &amp;amp; 2 \\ 8 &amp;amp; 2 \end{array}\right]"&gt; are &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-6" alt="-6" title="-6" data-latex="-6"&gt; and &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?4" alt="4" title="4" data-latex="4"&gt;.&lt;/p&gt;
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