Explain how to find the eigenvalues of the matrix \( \left[\begin{array}{cc} 7 & 2 \\ -4 & 1 \end{array}\right] \).
Answer:
The characteristic polynomial of \( \left[\begin{array}{cc} 7 & 2 \\ -4 & 1 \end{array}\right] \) is \( \lambda^{2} - 8 \lambda + 15 \).
The eigenvalues of \( \left[\begin{array}{cc} 7 & 2 \\ -4 & 1 \end{array}\right] \) are \( 3 \) and \( 5 \).