Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc} 5 & 2 \\ -10 & -7 \end{array}\right] \).
Answer:
The characteristic polynomial of \( \left[\begin{array}{cc} 5 & 2 \\ -10 & -7 \end{array}\right] \) is \( \lambda^{2} + 2 \lambda - 15 \).
The eigenvalues of \( \left[\begin{array}{cc} 5 & 2 \\ -10 & -7 \end{array}\right] \) are \( 3 \) and \( -5 \).