Homework
Only problems in bold will probably get graded, but turn in all the assigned problems. To receive full credit, you must always explain your answers, even if the problem doesn't ask for it. How detailed should your explanation be? Enough for a classmate who can't do the problem to be able to follow your solution.
Non-homework questions that may appear on exams
Final exam, T 5/3/11, 9:00-12:00, Fowler 301. The final exam will be cumulative, with some emphasis on the material after Midterm 3.
HW #32, due M 4/25: (this is our last HW assignment :) Read Sec 7.3 p.580-583 and Examples 7.25-7.28. Do: Sec 7.3: 1, 7, 15. Also do these additional problems. Post your review questions for the final exam here: Review questions. Solutions
HW #31, due F
4/22: Read Sec 2.4
Examples 2.33 and 2.34. Do: Sec 2.4: 23, 25, 26. Hint for 25: The
equation Ax=b has a solution iff b is in col(A); if A is symmetric,
then col(A)=row(rref(A)) (why?).
Solutions
Just for fun: the game of
Lights On. You can play the book's version of the game (just one
column of lights, as in class) by restricting attention to only the first
column of the 5x5 array in the "full version" of the game. Here's a
solution to the 5x5 game.
HW #30, due W 4/20: Read p.442-444. Do: Sec 6.1: 23, 26, 29, 30, 59, 61, 63, 64. Solutions Also read p.50-51; and do the following problems (but do not turn them in): Sec 1.4: 27, 29, 31. Solutions
HW #29, due M 4/18: Read Sec 6.1 up to Subspaces (p. 437); may skip Examples 6.7 & 6.8. Do: Sec 6.1: 1, 3, 5-9, 10, 61, 62. Solutions
Midterm 3, W 4/13: will cover HWs 18-28 and their corresponding sections, including all definitions in those sections (except the ones that were not part of the reading assignments), as well as non-homework questions listed at the link above. Here are the review questions you posted (no longer editable). Solutions
HW #28, due F 4/8: Read Sec 5.3 up to but not including QR Factorization. Do: Sec 5.3: 5, 7, 11, 12. Solutions
HW #27, due W 4/6: Read the rest of Sec 5.2. Do: Sec 5.2: 21, 24, 26. Also do these additional problems . Solutions Solutions-for-additional-problems
HW #26, due M 4/4: Read Sec 5.2 up to Orthogonal Projections. Do: Sec 5.2: 1, 3, 5, 23. Also do these additional problems. Solutions Solutions-for-additional-problems
HW #25, due F 4/1: Read Sec 5.1 up to but not including Orthogonal Matrices. Proofs of Theorems 5.1 and 5.2 may be on exams. Do: Sec 5.1: 1, 3, 7, 11, 12. Also do these additional problems. Solutions Solutions-for-additional-problems
HW #24, due W 3/30: Read Sec 4.4: p. 298-300 and Example 4.29. Proof of Theorem 4.22abde may be on exams. Do: Sec 4.4: 1, 3, 17, 18, 30, 31, 33, 34, 40, 41, 42. (On exams, for problems like 17 and 18 the matrix P would be provided.) Solutions
HW #23, due M 3/28: Read Sec 4.3. Do: 7, 13, 15, 16. Also do these problems: (i) Let A be an n x n matrix, E an eigenspace of A. Prove that E is a subspace of R^n by showing that it satisfies the definition of subspace. (Hint: start by writing down the definition of eignespace.) (ii) Prove or disprove: if A is singular, B is non-singular, then AB is singular. (Recall that "singular" means "not invertible".) (iii) Prove (without looking at the book or your notes) that a square matrix A is singular iff it has 0 as an eigenvalue. Solutions
HW #22, due F 3/25: Read Sec 4.2 up to Cramer's Rule. Also read about the Cross Product on p. 283. Optional: Area and Volume (p. 284) Do: Sec 4.2: 44, 49, 50, 51, 53, 54. Page 284: 2, 3a-e,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. (ii) Prove det A = 0 iff det rref(A) = 0. (iii) Use the above to show A is invertible iff det A is nonzero. Solutions (Sec 4.2) Solutions (p.284)
HW #21, due W 3/23: Read Sec 4.2 up to Determinants of Elementary Matrices. You should figure out proofs for Theorem 4.3a,c-f (ask me if you need help). Just for fun: Chimp playing Pacman. Do: Sec 4.2: 3, 13, 15, 17, 19, 20, 39, 40, 42. Typo in #20: should say "definition (3)". Solutions
HW #20, due M 3/21: Read Sec 4.1 (skip the last two examples). Do: 3, 7, 19, 21, 22, 23. Also turn in these extra problems. Solutions
HW #19, due F 3/18: Read Sec 3.5 p.199-205. Do: Sec 3.5: 38, 39, 40, 41, 47, 55, 56. Hint for 56: Use FTIM. Solutions
Midterm 2: W 3/16. The exam will cover HWs 10-17 and their corresponding sections, plus non-homework questions listed at the link above. Here's a copy of my 2007 Midterm2 with solutions. But our exam will cover a slightly different set of sections. The best way to study for the exam is to review homework problems; do the hardest ones (closed book and notes). Solutions
HW #18, due M 3/14: Read Sec 3.5 Examples 3.45-3.47. Do: Sec 3.5: 18, 19, 22, 23, 25, 40, 48. In 18-23 ignore null(A). For #22 and 23, read the middle paragraph of p.198. Hint for #48: Add the vectors! (Note: the answer in the back of the book to #48 is incorrect.) In all problems you may use a calculator or computer for tedious computations to find rref. Solutions
HW #17, due F 3/4: Read Sec 3.5 up to and including Example 3.44. May skip those parts of Example 3.41 that deal with the vector w. Proof of Theorem 3.19 may be on exams. Review Problem 21 of Section 2.3 (problem from HW#10). It's important that you understand and remember it well. Do: Sec 3.5: 11 (only for col(A)), 13, 33, 34, 39, 45, 49. Solutions ; Solutions for 39, 45, 49.
HW #16, due W 3/2: Read Sec 3.5 up to and including Example 3.40. Do: Sec 3.5: 1, 2, 3, 5, 6, Solutions
HW #15, due M 2/28: Read Sec 3.3: Elementary Matrices, and The Fundamental Theorem of Invertible Matrices. Example 3.28 will help with problems 35-38 of the homework. Do: Sec 3.3: 25, 27, 35, 36, 37, 38, 39, 45, 46. Solutions
HW #14, due F 2/25:
Read Sec 3.3 up to Elementary Matrices, plus The
Gauss-Jordan Method for Computing the Inverse. Proofs of Theorems 3.6 and
3.9(a-d) may be on exams. Do: Sec 3.3:
14,15,
16, 21, 22,
23, 25, 27, 43,
49,
59. Solutions
HW #13, due W 2/23: Read Sec 3.2, but skip Examples 3.16-3.18. Proof of Theorem 3.4(d) may be on future exams. Sec 3.3 up to Properties of Invertible Matrices. Sec 3.2: 30, 34, 35, 36, 44. Sec 3.3: 3, 11, 19. Solutions
HW #12, due F 2/18: Read Sec 3.1: p. 143-150; no need to memorize what "outer product" is (p. 145). Do: Sec 3.1: 13, 17, 23, 24, 29, 30, 31, 39c, 41. Solutions
HW #11, due W 2/16: Read Sec 3.1: up to Partitioned Matrices. Do: Sec 3.1: 1, 3, 5, 11, 18, 19, 20, 21. Sec 2.3: 33, 42, 45. Solutions
HW #10, due M 2/14: Read Sec 2.3: Linear Independence. Do: Sec 2.3: 11, 20, 21, 25, 27, 28. In #20, for the definition of subset (the "horseshoe-like symbol"), see Appendix A (p. 634-635) or see Wikipedia. Solutions
Midterm 1: Friday 2/11/11. The exam will cover HWs 1-9 and their corresponding sections. Here's a copy of my 2007 Midterm1 and here are the solutions for it. But keep in mind that it didn't cover Sec 2.3, which our exam will (up to p.94). I suggest spending most of your time re-doing the hardest problems from HWs 1-9 (with your book and notes closed!); don't spend much time on the 2007 exam. Our exam may contain some multiple-choice questions. Solutions
HW #9, due W 2/9: Read Sec 2.3, up to Linear Independence (p.90-94). Do: Sec 2.3: 1, 3, 8, 9, 10, 13, 15, 18, 19. May use calculator or computer for tedious computations in finding rref: http://faculty.oxy.edu/rnaimi/home/onlineTools.htm. Solutions
HW #8, due M 2/7: Read Sec 2.2: Rank and Homogeneous Systems; skip "Linear Systems over Zp." Do: Sec 2.2: 11, 23(1,3,5,7), 35, 37, 41, 47, 49. Solutions
HW #7, due F 2/4: Read Sec 2.2 up to Homogeneous Systems; but ignore "Rank" for now. Do: Sec 2.2: 1-9(odds), 16, 19, 21, 25, 27. Solutions
HW #6, due W 2/2: Read Sec 2.1. Do: Sec 2.1: 1, 3, 11, 13, 15, 17, 23, 28, 29, 32, 34, 35. Solutions
HW #5, due M 1/31: Read the rest of Sec 1.3. Do: Sec 1.3: 7, 13, 18abcd , 19, 29, 33. (Hint for #33: see Example 1.26.) Solutions
HW #4, due F 1/28: Read Sec 1.3 up to "Planes in R^3", plus Example 1.25. It'll help you if you also preview the rest of Sec 1.3 before Wednesday's class. Sec 1.3: 1, 5, 11, 15, 16, 23, 28. Solutions
HW #3, due W 1/26: Read Sec 1.2, Projections (p. 24-25). ec 1.2: 31, 41, 54, 62-64. For 41 see Figure 1.36. At first try to do 64 without reading the hints below. Then read these hints: Hint for 64a: First explain why proj_u(v) is a scalar multiple of v. Then prove that if c is any scalar, proj_u(cu) = cu. Hint for 64b: Use 63. Solutions
HW #2, due M 1/24: Read Sec 1.2 up to projections; may skip the proof the Theorem 1.5. Pay attention to the remarks on page 16. Also read page xxiii (before Section 1); it has some really good advice. Do: Sec 1.2: 5,11,17, 25, 44, 47, 48, 52. (Solutions for this HW will be posted on Wednesday.) Solutions
HW #1, due F 1/21: Read Sec 1.1. Advice: Read the entire section, not just what seems necessary for the HW problems; otherwise you'll miss the "big picture." Do: Sec 1.1: 1d, 2d, 3c, 4c, 5a, 6, 9, 15, 17, 20, 23, 24. Solutions