0000.tex

\begin{exercise}{G3}{Eigenvalues}{0000}
\begin{exerciseStatement}

Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc}
-2 & 1 \\
18 & 1
\end{array}\right] \).

\end{exerciseStatement}
\begin{exerciseAnswer}

The characteristic polynomial of \( \left[\begin{array}{cc}
-2 & 1 \\
18 & 1
\end{array}\right] \) is \( \lambda^{2} + \lambda - 20 \).



The eigenvalues of \( \left[\begin{array}{cc}
-2 & 1 \\
18 & 1
\end{array}\right] \) are \( -5 \) and \( 4 \).

\end{exerciseAnswer}
\end{exercise}