Homework |
Problems appearing in boldface should be turned in. I encourage you to also turn in non-boldface problems, even though they won't get graded! The non-boldface problems are as important as the boldface ones. The only reason some are bold and some aren't is that the grader doesn't have time to grade all of them. But you should know how to do all of them.
Explain your work: You should always explain your work, even if the book doesn't ask you to. How much detail should you include? Enough so that a classmate who doesn't know how to do the problem could follow and understand your work.
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HW # |
Due | Read | Do |
|---|---|---|---|
| W 12/12/07 8:30-11:30AM. | Start reviewing for the final as soon as you can. The final will be cumulative, with
some emphasis on HWs 28-32. Here is the 2005 final exam if you want more practice; but ignore problems 3 and 9 and all of section 4 of this exam. (Sorry, I don't have any solutions written up for this exam). Proofs of theorems 3.4d, 3.6, 3.9a-d, 3.19, 3.31, 4.6, 5.1, 5.2 may be on the final exam (plus of course theorems whose proofs were assigned as homework). On the exam you will be given a list of the 10 axioms in the definition of Vector Space. I will be available for questions M 12/10 1-4pm and T 12/11 9:30am-3:30pm (except possibly during lunch time). |
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32 |
W 12/5 (Last day of classes) |
Read the definition of Subspace, Theorem 6.2, and Examples 6.10 and 6.13. Skim the rest of Sec 6.1. | Sec 6.1: 22, 23, 63, 64. Solutions |
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31 |
M 12/3 | Read Sec 6.1 up to Subspaces (p. 437); may skip Examples 6.7 & 6.8. | Sec 6.1: 1, 3, 5-9, 10, 61, 62. Solutions |
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-- |
F 11/30 | No homework! Instead you can preview Section 6.1 before we cover it in class on Friday (it's a somewhat abstract section, so a preview would be especially helpful). | None |
|
30 |
W 11/28 | Read page 47. Read Sec 2.4
Examples 2.33 and 2.34. 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 of Lights On. |
Sec 2.4: 23, 25, 26. Hints for 25: 1. The equation Ax=b has a solution iff b is in col(A). 2. If A is symmetric, then col(A)=row(rref(A)) (why?). Solutions |
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29 |
M 11/26 | Read Sec 7.3 p.580-583 and Examples 7.25-7.28. | Sec 7.3: 1, 7, 15. Also do these additional problems. Solutions Solutions to the additional problems |
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28 |
M 11/19 |
Read Sec 5.3 up to The QR Factorization. | Sec 5.3: 1,
7, 11. (In case it's hard to see: 7 and 11 are both
in boldface.) Also do these additional problems. Solutions Solutions to the additional problems |
| F 11/16 | Covers Homeworks 16-27. Start reviewing a week in advance. Midterm 3 from 2004 (ignore problem 8 and EC problems); here are the Solutions for it. NOTE: this old midterm is not meant to be representative of what our midterm will be like; it is only to give you extra practice. You should first concentrate on the HW problems and the theorems whose proofs I've asked you to learn for exams: Theorems 3.19, 4.6, 5.1, 5.2. |
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27 |
M 11/12 | Read the rest of Sec 5.2. | Sec 5.2: 21. Also do these additional problems. Solutions Solutions to the additional problems |
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26 |
F 11/9 | Read Sec 5.2 up to Orthogonal Projections. | Sec 5.2: 1, 3, 5,
23, 26. Also do these additional problems. Solutions Solutions to the additional problems |
|
25 |
W 11/7 | Read Sec 5.1 up to but not including Orthogonal Matrices. Proofs of Theorems 5.1 and 5.2 may be on exams. | Sec 5.1: 1, 3, 7, 11, 12. Also do these additional problems. Solutions (Sec 5.1) Solutions (additional problems) |
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24 |
M 11/5 | Sec 4.2 up to Cramer's Rule. Proof of Theorem 4.6 may be on exams (you
may learn the proof given in the book or the one from class). Also read about the Cross Product on p. 283. Optional: Area and Volume (p. 284). |
Sec 4.2: 44, 49,
50, 51, 53,
54. Page 284: 2, 3a-f. Solutions (Sec 4.2) Solutions (P.284) |
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23 |
F 11/2 | Sec 4.2 up to Determinants of Elementary Matrices Chimp playing Pacman |
Sec 4.2: 3, 13, 15, 17,
19, 20,
30, 33, 39,
40. Typo in #20: should say "definition (3)". Solutions |
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22 |
W 10/31 | Sec 4.1 (skip the last two examples).
Here are some websites you can "play" with if you like: |
Sec 4.1: 3,
7, 13-15, 17,
18, 19, 21,
22,
23. Also turn in these extra problems. Solutions Solutions to extra problems |
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21 |
M 10/29 | Sec 3.6: Example 3.59 to the end of the section. Proof of Theorem 3.31 may be on future exams. | Sec 3.6: 37, 44, 47, 49, 51, 54, 55. (Problem 54 is easy but important.) Solutions |
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20 |
F 10/26 | Sec 3.6 up to and including Example 3.59 part (a). | Sec 3.6: 1,
5,
9, 13, 17, 19, 21,
25. Solutions |
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19 |
W 10/24 | Sec 3.5 p.199-205. | Sec 3.5:
38, 39, 40,
41, 47, 55,
56, and
these extra problems. Hint for 56: Use FTIM. EC: 62. Solutions Solutions to the extra problems |
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18 |
M 10/22 | Sec 3.5 Examples 3.45-3.47 | Sec 3.5: 18-21, 25,
34,
48. Do problems 18-21 for row(A) and col(A) only, not for null(A). For #21, 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 may use calculator or computer for tedious computations to find rref. Solutions |
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Mid 2 |
F 10/19 | Covers HWs 7-15 and their corresponding sections. Start reviewing a week in advance. Here's my 2005 Mid 2 if you want you to test yourself. |
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17 |
W 10/17 | 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. |
Sec 3.5: 11-14, 17, 33. Solutions |
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16 |
F 10/12 | Sec 3.5 up to and including Example 3.40. | Sec 3.5: 1,
2, 3, 5,
6, 7, 10. Solutions |
|
15 |
W 10/10 | Sec 3.3: The Fundamental Theorem of Invertible Matrices. Example 3.28 will help with problems 35-38 of the homework. |
Sec 3.3: 35-37,
38, 39, 45,
46. Solutions |
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14 |
M 10/8 | Sec 3.3 up to The Fundamental Theorem of Invertible Matrices, plus The Gauss-Jordan Method for Computing the Inverse. Proofs of Theorems 3.6 and 3.9(a-d) may be on exams. | Sec 3.3:
14,15, 16, 21,
22, 23, 25, 27, 43,
49,
59. Solutions |
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13 |
F 10/5 | 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 |
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12 |
W 10/3 | Sec 3.1: p. 143-150; no need to memorize what "outer product" is (p. 145). | Sec 3.1: 13, 17, 23,
24, 29, 30, 31, 39c,
41. Solutions |
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11 |
M 10/1 | Sec 3.1: up to Partitioned Matrices. | Sec 3.1: 1, 3, 5,
18, 19,
20, 21. Solutions |
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10 |
F 9/29 | Sec 2.3: Linear Independence. | Sec 2.3: 11,
20, 21, 25, 27,
28, 35, 37, 38,
42,
45. In #20, for the definition of subset (the "horseshoe-like symbol"), see Appendix A (p. 634-5) or see wikipedia. May use calculator or computer for tedious computations in finding rref. Solutions |
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9 |
W 9/26 | Sec 2.3, up to Linear Independence. | Sec 2.3: 1, 3,
8, 9,
10, 13,
15, 18, 19. May use calculator or computer for tedious computations in finding rref: The Linear Algebra Toolkit. Solutions |
|
8 |
M 9/24 | Sec 2.2: Rank and Homogeneous Systems; skip "Linear Systems over
Zp . Check out this great webpage: The Linear Algebra Toolkit. |
Sec 2.2: 11, 23(1,3,5,7), 35, 37,
41, 47,
49. EC: 50. Solutions |
| F 9/21 | Covers HWs 1-6 and their corresponding sections. Start reviewing a week in advance. Make sure you can do every HW problem on your own without looking at the book, your notes, or any solutions. Once you think you're ready for the exam, try Fall 2005's mid 1. Here are the solutions for the Fall 2005 mid 1. |
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|
7 |
W 9/19 | Sec 2.2 up to Homogeneous Systems; but ignore "Rank" for now. | Sec 2.2: 1-9(odds),
16, 19, 25, 27. EC: Sec 1.2: 67; Sec1.3: 47. Solutions |
|
6 |
M 9/17 | Sec 2.1. | Sec 2.1: 1, 3, 11, 13, 15, 17, 23, 28, 29,
32, 34, 35. Solutions |
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5 |
F 9/14 | Read the rest of Sec 1.3. | Sec 1.3: 7,
13,
18, 19,
29,
33. Solutions |
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4 |
W 9/12 | Sec 1.3 up to "Planes in R^3", plus Example 1.25. It'll be good for 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 |
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3 |
M 9/10 | Sec 1.2, Projections (p. 24-25). | Sec 1.2: 31,
41, 54, 62-64. At first try to do 64 without reading the hints below. Then read these hints: Hint for 64a: First explain why proju(v) is a scalar multiple of v. Then prove that if c is any scalar, proju(cu) = cu. Hint for 64b: Use 63. Solutions |
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2 |
F 9/7 | Sec 1.2 up to projections; may skip the proof the Theorem 1.5. Pay
attention to the bottom of page 16 about the meaning of "if and only
if." Also read page xxiii (before Section 1); it has some really good advice. |
Sec 1.2: 5,11,17, 25,
44,
47,
48, 52. EC: 58. Solutions |
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1 |
W 9/5 | Sec 1.1. Preview 1.2. Advice: Read the entire section, not just what's necessary for the HW problems; otherwise you'll miss the "big picture." |
Sec 1.1: 1d, 2d, 3c, 4c, 5a, 6, 9, 15, 17,
20, 23, 24. EC: 14. Solutions |
EC: Extra Credit problems are optional, and do not carry any points. If you do them, do not turn them in with your regular homework; you can show them to me during office hours. These are problems that are fun and sometimes more challenging. Work on them only if you have already mastered all the other problems.