Linear Algebra. Math-4100, Fall 2007
Assignment 2
Due Thursday, September 20, by 4pm. (Either in class, or my mailbox in AE 301, or
under my door AE 405).
Reading
Sep. 10 and 13: Strang Sections 3.1–3.3.
Sep. 17 and 20: Strang Sections 3.4–3.5.
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. Read worked example 2.7 B. Don’t hand in anything for this problem.
The next two problems contain some simple questions; write brief justifi-
cations/calculations to support your answers.
2. Problem 2.7 #7, 16, 19.
3. Problem 2.7 #37.
4. Read worked example 3.1 A. Don’t hand in anything for this problem.
5. Problem 3.1 #10.
6. Problem 3.1 #24.
7. Problem 3.1 #27.
8. Problem 3.2 #5.
9. Problem 3.2 #7.
10. Problem 3.2 #17, 18.
11. Problem 3.2 #21.
12. Problem 3.2 #31.
13. Problem 3.3 #2(b).
14. Problem 3.3 #17.
E2. (Extra credit) Prove that no reordering of columns and reordering of rows can trans-
pose a typical matrix.
E3. (Extra credit) Suppose Aand Bare n×nmatrices, and Bis a right inverse of A, i.e.,
AB =I. Prove that Ais invertible and therefore Bis also the left inverse of A. A way to
prove it is indicated in problems 3.3 17-19. A related (and a bit tricky) question , if C D =I
is it true that DC =I? See Problem 3.3 #20.