0011.ptx

<exercise checkit-seed="0011" checkit-slug="G3" checkit-title="Eigenvalues">
  <statement>
    <p>Explain how to find the eigenvalues of the matrix <m> \left[\begin{array}{cc}
5 &amp; 1 \\
-20 &amp; -7
\end{array}\right] </m>.</p>
  </statement>
  <answer>
    <p>The characteristic polynomial of <m> \left[\begin{array}{cc}
5 &amp; 1 \\
-20 &amp; -7
\end{array}\right] </m> is <m> \lambda^{2} + 2 \lambda - 15 </m>.</p>
    <p>The eigenvalues of <m> \left[\begin{array}{cc}
5 &amp; 1 \\
-20 &amp; -7
\end{array}\right] </m> are <m> 3 </m> and <m> -5 </m>.</p>
  </answer>
</exercise>