Exercise 9

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

1. Find the eigenvalues and associated eigenvectors of $A$.

2. Make a prediction about what happens if we apply the power method and the inverse power method to find eigenvalues of $A$.

3. Verify your prediction using Sage.