1. Show that for the given matrices, in other words, in other words, show that is diagonalizable.
  1. Determine whether or not is diagonalizable. If so, find and such that .
    a.


    Only one eigenvalue

A is not diagonolizable

b.

c.

d.
3. Compute where .
4. Suppose that a matrix has eigenvalues . Compute .
5. Find a matrix whose eigenvalues are and associated eigenvectors are .
6. Suppose that are eigenvalues of a matrix with associated eigenvectors and . Prove that for .