HW11 - Math 136 Assignment 11 NOT TO BE HANDED IN 1 For...

Math 136: Assignment 11
NOT TO BE HANDED IN
1. For each of the following matrices, find the eigenvalues and corresponding eigenvectors,
and also state the algebraic and geometric multiplicities of the eigenvalues.
(a) A =
2 7
7 2
(b) B =
7 - 2
2 3
(c) C =


5 - 2 3
0 1 0
6 7 - 2



- 1 0 1
- 3 4 1

2. Verify that each column of P is an eigenvector of A , and determine the corresponding
eigenvalues. Check that the rank of P is 3, so the columns are linearly independent. Hence
(without further calculation), determine P - 1 AP .


- 7 2 - 4
8 - 1 4
18 - 6 11


,