Last Edited: 7-21-09, 11:54am.
Final Review Materials
July 20 : These problems are optional (they will not be collected), but strongly recommended.
SVD:
Sec 6.5, p. 369: 1, 2 (b), (c), 5 (will need to read a bit about SVD for rectangular matrices).
Linear Transformations:
Sec. 4.1, p. 182: 1 (a), (b), (d), 5 (b), (c), (d), 6 (a), (b), (d), 15
Sec 4.2, p. 196: 1 (a), (b), (d), 2, 6
Change of Basis:
Sec 3.5, p. 161: 1, 5, 7, 8
July 17: Sec 6.6, p. 383: 1, 7 (a), (c), (e), 13
Sec. 6.7, p. 390: 13
Jordan Canonical form question: Suppose a 5x5 matrix A has eigenvalues 3,3,3,2,2. What are all the possible Jordan Canonical forms for A? (Hint: Two Jordan matrices are similar if they are only different up to a rearrangement of the Jordan blocks. There should be 6 different (i.e. non-similar) matrices.
July 15: Sec. 6.7, p. 390: 1, 3, 8
Sec. 5.5, p. 271: 10
Due Monday, July 20.
Review for midterm 2
I'd recommend doing this problem set before taking the midterm, so you have adequate practice with these techniques.
July 6: Sec. 6.3, p. 340: 20, 21, 27, 28 (a) (b)
Sec. 5.5, p. 270: 27
Due Wednesday, July 15
June 29: Sec. 2.3, p. 109: 1, 2
Sec. 6.1, p. 310: 1 (a),(d),(g),(j), 2, 4, 10, 11
Due Monday, July 6
June 26: Since some of you already appear to be comfortable with determinants, I am offering you a choice of problems this week: the first is what I would've given, and is mostly routine computation; the second is more theoretical, with fewer "routine" problems. I have tried to make the total difficulty of the two the same.
Option 1:
Sec. 2.1, p. 96: 2, 3, 4
Sec. 2.2, p. 103: 3, 4, 7, 12, 13
Option 2:
Sec. 2.1, p. 96: 4, 5, 6, 13 (note this is similar, but not the same as the example in class, since the matrix is not just 1's)
Sec. 2.2, p. 103: 2, 7, 12, 13
Due Wednesday, July 1.
This problem set is a bit long, but it is important to get practice with this.
June 24: Sec. 5.1, p. 223: 3, 5, 6, 7, 9
Sec. 5.2, p. 233: 2 (note: S&perp is the orthogonal complement of S.), 3, 6
Sec. 5.3, p. 243: 1, 2 (note: r(x) is what we called e .)
Sec. 5.5, p. 270: 1, 21
Sec. 5.6, p. 281: 1, 2, 3, 5, 8
Due Monday, June 29.
June 15: Sec. 3.6, p. 167: #10, 12, 13 (Note: an and xn are column vectors of A) Also this bit extra . There are some helpful notes for the problem set for today's class here
Due Friday, June 19
June 12: Sec. 3.4, p. 150: #3, 5, 7
Sec. 3.6, p. 167, #1, 2, 7, 8, 16
Due Wednesday, June 17.
June 10: Sec. 3.1, p. 122- #6
Sec. 3.2, p. 131- #1, 2, 4, 20
Sec. 3.6, p. 167- #4
Due Monday, June 15.
The last example from today's lecture
June 8: Sec. 1.3, p. 57- # 7, 11;
Sec. 1.4, p. 69- # 8, 9, 10 (b)(c)(f)(g) , 19, 22
Due Friday, June 12.
Note: A copy of Leon's text will be in office HB14 on my desk (the messy one with googly eyes and a sombrero). You are welcome to use it, but please don't take it out of the office (the office is gigantic with plenty of workspace).
June 1: Problem set 1
These should help with part of problem set 1: Lecture notes from June 1
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