Math 247F - Homework 5, Due on Tuesday, October 17

1. Section 6.4: #2 b, d, e, 4,  8,  16, 17
   
2. Section 6.5:  1,  2a,d, 3, 4
   
3. Let T be a linear  map from a  finite dimensional vector space V into itself. Prove that if  W is a T-invariant subspace of V then the characteristic polinomial of T| _W  divides the characteristic polynomial of T.

Extra credit:  Prove that any polynomial with real coefficients splits over R into factors of degree at most 2. You can use the fundamental theorem of algebra which says that any complex polynomial splits into factors of degree 1.

Do NOT do the other problem that I posed in class that isometries of R^k are linear. That problem is solved in the book.