Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc} 10 & 2 \\ -27 & -5 \end{array}\right] \).
Answer:
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 \( 1 \).