0007.ptx

<exercise checkit-seed="0007" checkit-slug="G3" checkit-title="Eigenvalues">
  <statement>
    <p>Explain how to find the eigenvalues of the matrix <m> \left[\begin{array}{cc}
10 &amp; 2 \\
-27 &amp; -5
\end{array}\right] </m>.</p>
  </statement>
  <answer>
    <p>The characteristic polynomial of <m> \left[\begin{array}{cc}
10 &amp; 2 \\
-27 &amp; -5
\end{array}\right] </m> is <m> \lambda^{2} - 5 \lambda + 4 </m>.</p>
    <p>The eigenvalues of <m> \left[\begin{array}{cc}
10 &amp; 2 \\
-27 &amp; -5
\end{array}\right] </m> are <m> 4 </m> and <m> 1 </m>.</p>
  </answer>
</exercise>