0004.tex

\begin{exercise}{G3}{Eigenvalues}{0004}
\begin{exerciseStatement}

Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc}
7 & 1 \\
-18 & -4
\end{array}\right] \).

\end{exerciseStatement}
\begin{exerciseAnswer}

The characteristic polynomial of \( \left[\begin{array}{cc}
7 & 1 \\
-18 & -4
\end{array}\right] \) is \( \lambda^{2} - 3 \lambda - 10 \).



The eigenvalues of \( \left[\begin{array}{cc}
7 & 1 \\
-18 & -4
\end{array}\right] \) are \( 5 \) and \( -2 \).

\end{exerciseAnswer}
\end{exercise}