Consider the matrix \(A = \left[\begin{array}{rr} 0 \amp -1 \\ -4 \amp 0 \\ \end{array}\right] \text{.}\)

  1. Describe what happens if we apply the power method and the inverse power method using the initial vector \(\xvec_0 = \twovec{1}{0}\text{.}\)

  2. Find the eigenvalues and eigenvalues of this matrix and explain this observed behavior.

  3. How can we apply the techniques of this section to find the eigenvalues of \(A\text{?}\)