###### Exercise4

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 of this matrix and explain this observed behavior.

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

in-context