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