Reminder: I am usually available for questions MWF before class and at 4pm; but I need to know in advance if you'd like to meet with me. Professor Tollisen is also available MTThF, 2-5pm (12 hours per week!) in Library 17.
Final Exam F 5/5, 1pm. The final exam will cover all homework assignments. In addition to homework problems, I may also ask you to give definitions, and to prove one or more of the following theorems on the final exam: 5.9acd; 5.2; 5.1; 4.22abde; 4.9; 3.19; 3.9(a-d); 2.5.
For M 5/1: Review all problems in HWs 25-30 and bring questions to class.
For F 4/28: Review all problems in HWs 18-24 and bring questions to class.
For W 4/26: Review all problems in HWs 11-17 and bring questions to class.
For M 4/24: Review all problems in HWs 1-10 and bring questions to class.
HW 30, due F 4/21. Read Sec 2.4 Examples 2.35 and 2.36. Do Sec 2.4: 29, 31, 32. Also do these extra problems.
HW 29, due W 4/19. Read Sec 5.3 p.388-392. Do Sec 5.3: 1, 3, 5, 7, 11, 12. Also do these extra problems.
Ignore HW 28 for now. We'll come back to it later. HW 28, due W 4/19. First do these extra problems, then do Sec 5.2: 30.
HW 27, due M 4/17. Read Sec 5.2 p.384-386. Do Sec 5.2: 19, 21, 27-29. Also do these extra problems. Hint for #27: first show proju(v+w)=proju(v)+proju(w). Before doing #29, do #2 in the extra problems.
HW 26, due F 4/14. Read Sec 5.2 p.382-383 to the end of Example 5.11. Do Sec 5.2: 9, 15, 17, 23-26. Also do these extra problems.
HW 25, due W 4/12. Read Sec 5.2 p.378-381. If you find this section difficult, read the book slowly, more than once if necessary, and think "patiently" while reading. Do Sec 5.2: 1, 3, 5, 11. Also do these extra problems.
HW 24, due M 4/10. Read Sec 5.1 p.368-373. Do Sec 5.1: 7, 13. Also do these extra problems.
HW 23, due F 4/7. Read Sec 4.4; may skip Theorem 4.24, Lemma 4.26, and Theorem 4.27. Do Sec 4.4: 1, 9, 17, 30-33, 36, 42-44. Hint for 33 32: use Sec 3.5 problem 61 (even though we didn't do #61).
HW 22, due W 4/5. Read Sec 4.3. Do Sec 4.3: 13, 14, 17-19, 22, 24, 25.
HW 21, due M 4/3. Read Sec 4.2 up to Cramer's Rule. Also read about the Cross Product on p. 286. The subsection on Area and Volume (p. 287) is optional. Do: Sec 4.2: 19, 47, 49, 51, 53, 54, page 287: 3a-f. Also do these problems: (i) Prove that if B is obtained from A by one elementary row operation, then det A = 0 iff det B = 0; you may use Theorem 4.3 for this. (ii) Prove det A = 0 iff det rref(A) = 0; you may not use FTIM for this. (iii) Use (i) and (ii) above to show A is invertible iff det A is nonzero.
Midterm 2, F 3/31. The exam will cover HWs 12-20. The best way to review for the exam is to redo all homework problems, especially those that you couldn't do on your own and had to get help (or look at the solutions) for them. Make sure you can do the problems without looking at your notes or the book.
HW 20, due W M 3/27. Read Sec 4.2 p.263-272. Do Sec 4.2: 7, 10, 15, 20, 26, 27, 32, 35, 37, 39-41, 45.
HW 19, due F 3/24. Read Sec 4.1. Do Sec 4.1: 3, 7, 13-19, 21-23, 35a, 37. Also do this problem: Prove, from definitions, that each eigenspace of an n x n matrix is a subspace of R^n (without using the paragraph at the bottom of page 255).
HW 18, due W 3/22. Do Sec 3.5: 41-43, 53, 65. For #65, use the following theorem (the book doesn't mention theorem): If S and S' are subspaces of R^n and S is a subset of S', then dim(S) <= dim(S').
HW 17, due M 3/20. Read Sec 3..5 p.203-206. Do Sec 3.5: 29, 31, 33, 34, 58. There are fewer problems than usual in this assignment; spend more time on reading the book carefully, including proofs of Theorems 3.24, 3.25, 3.26.
HW 16, due F 3/17. Read Sec 3.5 p.195-203. Do Sec 3.5: 11, 13, 15, 17, 27, 45, 49, 50, 57.
HW 15, due W 3/15. Read Sec 3..5 p.191-194. Do Sec 3.5: 1-10.
HW 14, due M 3/13. Read Sec 3.3 p.170-178. Do Sec 3.3: 25, 27, 29, 30, 37, 39, 45, 46, 49, 55, 61.
HW 13, due W 3/1. Read Sec 3.3 p.163-170. Do Sec 3.3: 3, 9, 11, 13, 14-16, 19, 41-43.
Reminder: you should spend an hour or more for each reading assignment. You should read the book slowly and think patiently. Sometimes you may need to read certain parts multiple times. Reading your class notes won't work as a substitute for reading the book.
HW 12, due M 2/27. Read Sec 3.2. Do Sec 3.2: 3, 5, 13, 22, 26, 28, 34, 35, 44.
Midterm1, W 2/22. The exam will cover HWs 1-11 and their corresponding sections. The best way to review for the exam is to redo all homework problems, especially those that you couldn't do on your own and had to get help (or look at the solutions) for them. Make sure you can do the problems without looking at your notes or the book.
My exam questions are always like homework problems, sometimes exact copies, but usually a little modified. (Except that on the final exam I sometimes include one problem that's not quite like homework problems.)
HW 11, due F 2/17. Read Sec 3.1; you may skip the subsection on partitioned matrices; but make sure to read Matrix Powers, and Transpose of a Matrix, including the definition of a symmetric matrix. There are no homework problems on these two topics, but I will assume you know them when I talk about Sec 3.2. Do Sec 3.1: 1, 5, 11, 17, 18, 21, 23, 29, 39ab. Problems 23 and 29 are hard but important; make sure you understand how to do them. Hint for 23 and 29: Colj(AB) = A Colj(B); and Ab = Col1(A) b1 + ... + Coln(A) bn, where bi is the ith coordinate of b.
HW 10, due W 2/15. Read Sec 2.3 p.92-97; may skip proof of Theorem 2.7. We didn't cover Theorem 2.5 in class, but make sure to read it carefully; it's important --- it's a useful way to understand and look at linear (in)dependence. On exams you may be asked to prove Theorem 2.5. Do Sec 2.3: 25-27, 42-44, 46, 47.
HW 9, due M 2/13. Read Sec 2.3 p.88-92. Do Sec 2.3: 1, 7, 9, 13, 15, 18-21. Problem 21(a) is very important. Even if you can't prove part (a), make sure you fully understand what it's saying. You will need to rely on the concept repeatedly later on. Doing part (c) may help you better understand parts (a) and (b).
HW 8, due F 2/10. Read Sec 2.2 p.76-79. Do Sec 2.2: 23, 39, 44, 45, 47, 49, 52-54, 60.
HW 7, due W 2/8. Read Sec 2.2 p.64-75. Do Sec 2.2: 1, 3, 5, 7, 9, 11, 16, 17, 19-21, 24, 29, 36, 41.
HW 6, due M 2/6. Read Sec 2.1. Do Sec 2.1: 1, 3, 15, 23, 24, 29, 30, 35, 36, 39, 41, 43.
HW 5, due F 2/3. Read Sec 1.3 p.38-44; don't memorize Equations (3) and (4); you may not even use them for doing any problems (neither on HW nor on exams --- even though the author uses them in the posted solutions). So make sure you can do problems like 32 and 33 of Sec 1.3 without using Equations (3) and (4)! Do Sec 1.3: 9, 13, 18, 19, 25, 33, 35, 37, 45, 47, 48c. I believe in 48 there is a typo: it should say Exercise 47 instead of 43.
HW 4, due W 2/1. Read: Sec 1.3 p.34-38. Do Sec 1.3: 1, 5, 12, 16, 17, 21, 23, 32, 41.
HW 3, due M 1/30. Read Sec 1.2 p.27-28. Do Sec 1.2: 64-70, 72.
HW 2, due F 1/27. Read Sec 1.2 p.18-26. Do Sec 1.2: 9, 17, 18, 24, 31, 32, 38-40, 50-53, 59-61. Problems without the CAS symbol should be done by hand (no calculator); you can't use calculators on the exams at all.
HW 1, due W 1/25. Read Sec 1.1 (if you haven't seen this material before, it may take over an hour to read and understand the entire section). Do Sec 1.1: 1c, 2, 4d, 9, 13, 14, 18, 24e, 29, 54, 57a. (For some of the even problems that you feel unsure about, it may help to do a similar odd problem that appears just before or after it so you can compare your answer with the back of the book.)