MAT 335

HOMEWORK ASSIGNMENT #12

HAND IN MONDAY, Dec. 3, 2007 (for feedback Wed., Dec. 5)

HAND IN WEDNESDAY, Dec. 5, 2007 (for feedback Wed., Dec. 12)

1. Let and

a) Is an eigenvector for A ?

b) Is an eigenvalue of A ?

2. Given

a) Find an eigenvector for A corresponding to the eigenvalue

b) A has another eigenvalue besides . Find it.

3. Find a basis for the eigenspace of corresponding to

4. Find all eigenvalues of

5. Let and

a) Calculate

b) Calculate the distance between and

c) Show that is orthogonal to

d) Calculate the projection of onto