Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc} 3 & 2 \\ 2 & 3 \end{array}\right] \).
Answer:
The characteristic polynomial of \( \left[\begin{array}{cc} 3 & 2 \\ 2 & 3 \end{array}\right] \) is \( \lambda^{2} - 6 \lambda + 5 \).
The eigenvalues of \( \left[\begin{array}{cc} 3 & 2 \\ 2 & 3 \end{array}\right] \) are \( 1 \) and \( 5 \).