Exercise 4

Consider the matrix $A = \left[\begin{array}{rr} 0 & -1 \\ -4 & 0 \\ \end{array}\right]$.

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

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 $A$?