###### Exercise 5

For the following matrices, find the eigenvectors and associated eigenvalues by thinking geometrically about the corresponding matrix transformation.

\(\left[\begin{array}{rr} 3 \amp 0 \\ 0 \amp 3 \\ \end{array}\right] \text{.}\)

\(\left[\begin{array}{rr} -2 \amp 0 \\ 0 \amp 4 \\ \end{array}\right] \text{.}\)

What are the eigenvectors and associated eigenvalues of the identity matrix?

What are the eigenvectors and associated eigenvalues of a diagonal matrix with distinct diagonal entries?