Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc} 9 & 2 \\ -22 & -6 \end{array}\right] \).
Answer:
The characteristic polynomial of \( \left[\begin{array}{cc} 9 & 2 \\ -22 & -6 \end{array}\right] \) is \( \lambda^{2} - 3 \lambda - 10 \).
The eigenvalues of \( \left[\begin{array}{cc} 9 & 2 \\ -22 & -6 \end{array}\right] \) are \( 5 \) and \( -2 \).