0002.tex

\begin{exercise}{G3}{Eigenvalues}{0002}
\begin{exerciseStatement}

Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc}
5 & 2 \\
-10 & -7
\end{array}\right] \).

\end{exerciseStatement}
\begin{exerciseAnswer}

The characteristic polynomial of \( \left[\begin{array}{cc}
5 & 2 \\
-10 & -7
\end{array}\right] \) is \( \lambda^{2} + 2 \lambda - 15 \).



The eigenvalues of \( \left[\begin{array}{cc}
5 & 2 \\
-10 & -7
\end{array}\right] \) are \( 3 \) and \( -5 \).

\end{exerciseAnswer}
\end{exercise}