0005.tex

\begin{exercise}{G3}{Eigenvalues}{0005}
\begin{exerciseStatement}

Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc}
-4 & 2 \\
8 & 2
\end{array}\right] \).

\end{exerciseStatement}
\begin{exerciseAnswer}

The characteristic polynomial of \( \left[\begin{array}{cc}
-4 & 2 \\
8 & 2
\end{array}\right] \) is \( \lambda^{2} + 2 \lambda - 24 \).



The eigenvalues of \( \left[\begin{array}{cc}
-4 & 2 \\
8 & 2
\end{array}\right] \) are \( -6 \) and \( 4 \).

\end{exerciseAnswer}
\end{exercise}