Linear Algebra. Math-4100, Fall 2007
Assignment 4
Due Thursday, October 11, by 4pm. (Either in class, or my mailbox in AE 301, or
under my door AE 405).
Reading
Sep. 24, Oct. 4: Strang Sections 4.1-4.3 and 4.4 (up to Gram-Schmidt, p.223).
Oct. 8, 11: Strang Sections 4.4, 5.1, 5.2; Gelfand Section 3.
Problems
You are welcome to consult the text and notes and discuss the problems with other people.
However, the solutions should be yours. Please indicated on your papers, who you discussed
the problems with. Please submit extra credit problems on a separate sheet of paper.
1. Problem 4.1 #22.
2. Problem 4.1 #26. Describe how you produce your matrix A.
3. Problem 4.2 #1(a) and the part of problem #3 which is related to #1(a).
4. (5 points) Find condition(s) on projection matrices P1and P2that guarantee their
sum P1+P2being also a projection matrix. What do these conditions mean for the
subspaces B1and B2on which the matrices project?
5. (5 points) Problem 4.2 #13.
6. (5 points) Problem 4.2 #17.
7. Problem 4.2 #19.
8. Problem 4.3 #5.
9. Problem 4.3 #12.
10. Problem 4.4 #4. Note that question (b) is somewhat silly, but it makes sense.
11. Problem 4.4 #23.
12. (5 points) Problem 4.4 #34 (see Example 3 of Section 4.4).