Homework Answers/Hints

Homework 3, due 9/17

32. Hint: Image is spanned by column vectors. Don't necessarily think square matrix here.
33. Try a linear transformation from R<sup>3 to R1.
44. a. Yes. Kernel is the set of solutions to some linear system. What does changing to rref do to the solutions of a linear system?
b. No. For example, look at a 2 x 2 matrix with all 1's in it.
48. a. If w is in the image of A, w=Av for some v. Plug in...
b. rank(A)=2 implies...? rank(a)=0 implies...?
c. Skip for now.
50. Yes. Think about this one, and ask if you're stuck.</sup>

Section 3.2

4. Yes.
6. a. Yes. b. No.
7. Yes. How do you get 0?
37. Think about projections.