I may ask you to prove one or more of the following theorems on the final exam:
5.9; 5.1; 5.2; 4.22abde; 4.9; 3.19; 3.9(a-d); 2.5.
Final Exam M Dec 12, 8:30am 9:00am. The exam will cover all HW problems and their corresponding sections, plus proofs of the theorems listed above, plus these extra problems.
HW due M 12/5. Redo problems in HWs 26-30, plus these extra problems for the final exam.
HW due F 12/2. Redo problems in HWs 21-25.
HW due W 11/30. Redo problems in HWs 13-20 and bring questions to class.
HW 30, due M 11/28. Read Sec 2.4 Examples 2.35 and 2.36. Do Sec 2.4: 29, 31, 32. Redo problems in HWs 1-12.
HW 29, due M 11/21. Read Sec 5.3 p.388-392. Do Sec 5.3: 1, 3, 5, 7, 11, 12. Also do these extra problems.
HW 28, due F 11/18. First do these extra problems, then do Sec 5.2: 30.
HW 27, due W 11/16. 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 M 11/14. Read Sec 5.2 p.382-383 to the end of Example 5.11. Do Sec 5.2: 9, 15, 17, 23-26.
HW 25, due F 11/11. Read Sec 5.2 p.378-381. Usually many students have a hard time with this section; so read the book slowly, with a lot of thinking, and more than once if necessary. Do Sec 5.2: 1, 3, 5, 11. Also do these extra problems.
HW 24, due W 11/9. Read Sec 5.1 p.368-373. Do Sec 5.1: 7, 13. Also do these extra problems.
Correspondence between Midterm 2 problems and HW problems.
HW 23, due M 11/7. 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: use Sec 3.5 problem 61.
Midterm 2, F 11/4. The exam will cover HWs 11-22 and their corresponding sections.
HW 22, due M 10/31. Read Sec 4.3. Do Sec 4.3: 13, 14, 17-19, 22, 24, 25.
HW 21, due F 10/28. 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.
HW 20, due W 10/26. 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 M 10/24. Read Sec 4.1. Do Sec 4.1: 3, 7, 13-19, 21-23, 1, 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 F 10/21. Do Sec 3.5: 41-43, 53, 61, 65. For #65, use the following fact (even though the book doesn't mention it yet): If S and S' are subspaces of R^n and S is a subset of S', then dim(S) is <= dim(S').
HW 17, due W 10/19. 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 M 10/17. Read Sec 3..5 p.195-203. Do Sec 3.5: 11, 13, 15, 17, 27, 45, 49, 50, 57.
HW 15, due F 10/14. Read Sec 3..5 p.191-194. Do Sec 3.5: 1-10.
HW 14, due W 10/12. 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 F 10/7. 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 slowly reading the book (excluding class notes).
HW 12, due W 10/5. Read Sec 3.2. Do Sec 3.2: 3, 5, 13, 22, 26, 28, 34, 35, 44.
HW 11, due M 10/3. Read Sec 3.1 (you may skip the subsection on partitioned matrices for now; we may cover it later; but make sure to read the two subsections after it: Matrix Powers, and Transpose of a Matrix). Do Sec 3.1: 1, 5, 11, 17, 18, 21, 23, 29, 39ab.
Midterm 1, F 9/30. The exam will cover HWs 1-10 and their corresponding sections. Start reviewing at least a week before; redo every homework problem (at least the ones you feel unsure about). The week of the exam I will be busier and will have time to check very few of your homework problems. Make sure you can do problems like 32 and 33 of Sec 1.3 without using Equations (3) or (4) of that section.
HW 10, due M 9/26. Read Sec 2.3 p.92-97; may skip proof of Theorem 2.7. On exams I may ask you to prove Theorem 2.5. Do Sec 2.3: 25-27, 42-44, 46, 47.
HW 9, due F 9/23. 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 W 9/21. Read Sec 2.2 p.76-79. Do Sec 2.2: 23, 39, 44, 45, 47, 49, 52-54, 60.
HW 7, due M 9/19. 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 F 9/16. Read Sec 2.1. Do Sec 2.1: 1, 3, 15, 23, 24, 29, 30, 35, 36, 39, 41, 43.
HW 5, due W 9/14. 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 M 9/12. Read: Sec 1.3 p.34-38. Do Sec 1.3: 1, 5, 12, 16, 17, 21, 23, 32, 41.
HW 3, due F 9/9. Read Sec 1.2 p.27-28. Do Sec 1.2: 64-70, 72.
HW 2, due W 9/7. 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).
HW 1, due F 9/2. 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.)
Reminder: I am usually available for questions every day after class and in the afternoon. Professor Tollisen is also available: MTThF, 2-5pm, in Library 17 (that's 12 hours per week!).