0007.tex

\begin{exercise}{G3}{Eigenvalues}{0007}
\begin{exerciseStatement}

Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc}
10 & 2 \\
-27 & -5
\end{array}\right] \).

\end{exerciseStatement}
\begin{exerciseAnswer}

The characteristic polynomial of \( \left[\begin{array}{cc}
10 & 2 \\
-27 & -5
\end{array}\right] \) is \( \lambda^{2} - 5 \lambda + 4 \).



The eigenvalues of \( \left[\begin{array}{cc}
10 & 2 \\
-27 & -5
\end{array}\right] \) are \( 4 \) and \( 1 \).

\end{exerciseAnswer}
\end{exercise}