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Homework |
| HW # | Due | Read | Do | ||||||||||||||
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| Mon 5/3 1:00-4:00 PM |
Most important: memorize and understand all definitions; then test
yourself to make sure you do! The exam will be cumulative (all HW problems), with a little emphasis on material covered since the last midterm (HW 26-32). You should be able to prove the theorems covered by the 2nd and 3rd midterms (see Mid 2 and Mid 3 below), plus Theorems 1a, 2, 5, and Corollary 6 of Section 5.2. Office hours: Thurs 10:30-3:00, Fri 9:30-3:00, Mon 9:30-12:00. Please call (x2550) or email me before coming. |
Here are some problems to practice. Don't necessarily try to do all of
them; there are too many. Just use them to find out which topics you
need to work on more. (Also, they are missing a few topics, most
notably Least Squares Approximations.) In the following, "left null space" of a matrix A means null(A^T), i.e., the null space of the transpose of A. Practice Final Fall 2000 Final Spring 2000 Final |
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32 |
Wed 4/28 | Sec 2.4 Examples 7 and 8. | Don't turn in any of these problems: Play the game Lights On before doing problem 29 below (but don't play any other games on that website---study, instead!) Sec 2.4: 29. 1. Let P be the plane x+2y+3z=0. Find the projection of [1 1 1] onto P in two ways: (a) By finding and using an orthogonal basis for P. (b) By finding a matrix A whose column space is P, and then solving the equation A^T A x = A^T b. |
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31 |
Mon 4/26 | Sec 1.4 Examples 6 and 7. | Don't turn in any of these problems: Sec 1.4: 1, 9. Do also these review problems |
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30 |
Fri 4/23 | Sec 7.3 pages 581-587 to the end of Example 6 (skip proof of Theorem 2). Cross Product: pages 280-281. |
Sec 7.3: 7, 15. Page 47: 1a, 3, 4a, 5(hint: use Theorem 3 of Sec 4.2). |
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29 |
Wed 4/21 | Sec 7.3 pages 575-580 (skip proof of Theorem 1). In
Definition 1 and Theorem 1 you don't need to know what
"normed linear space" and "inner product space"
mean; think of them as just R^n.
Start reviewing for the final! It will be cumulative, with a little
emphasis on material covered since the last midterm. Start with
Sec 1.1 and each day spend at least half an hour to review a couple
of sections and their HW problems. |
Sec 7.3: 1. Sec 1.3: 31. Sec 3.2: 35. |
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28 |
Mon 4/19 | Sec 5.3 pages 375-379 (skip proof of Theorem 1). Also read proof of Theorem 1a of Sec 5.2. |
Sec 5.3: 1, 5, 7. Sec 5.2: 23, 24. |
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27 |
Fri 4/19 | Sec 5.2 pages 368-373 (including proofs of Theorem 5 and Corollary 6). | Sec 5.2: 17, 21, 25, 26. | ||||||||||||||
| Wed 4/14 | Covers HW 16-25, Sections 3.4-5.1 (except for skipped material). You should also be able to prove the following theorems:
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Mon 4/12 | Review for the midterm and bring questions to class. | |||||||||||||||
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26 |
Fri 4/9 | Sec 5.2 pages 364-368 (including proofs of Theorems 1a and 2). (We're skipping the second half of Sec 5.1, for now.) |
Sec 5.2: 1, 3, 5, 9, 13, 23, 24. (May use the link above
for finding rref of any matrix.) Also, justify the first sentence in the proof of Theorem 2. |
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25 |
Wed 4/7 | Sec 5.1 pages 353-358 (including proofs of Theorems 1-3). Start reviewing for Mid 3. |
Sec 5.1: 1, 3, 7, 11, 12. Sec 4.4: 7. Also, practice writing proofs of Theorems 1 and 2 of Sec 5.1 and Theorem 11 of Sec 3.4 a few hours after reading them in the book or your notes. |
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24 |
Mon 4/5 | Sec 4.4 pages 296-300, plus Example 8; also read the proof of Theorem 2ad. (Extra Credit: proof of Theorem 3.) | Sec 4.4: 1, 3, 5, 9, 19, 30, 31, 33. EC: 32. | ||||||||||||||
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23 |
Fri 4/2 | Sec 4.3 up to and including Example 4. Read the proof of Theorem 2 (but the other proofs are optional). | Sec 4.3: 5, 13, 15, 16, 19, 22, 24. | ||||||||||||||
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22 |
Wed 3/31 | Sec 4.2 pages 264-265 (including proof of part d of Theorem 3), Theorems 6-8 without proofs, and Theorems 9-10 with proofs. | Sec 4.2: 30, 33, 39, 40, 41, 53, 54. EC: 42. | ||||||||||||||
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21 |
Mon 3/29 | Sec 4.2 pages 256-264. | Sec 4.2: 3, 13, 15, 17, 19, 20. EC: 21. | ||||||||||||||
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20 |
Fri 3/26 | Sec 4.1, but skip Examples 6 and 7. | Sec 4.1: 3, 7, 13, 17, 19, 21, 23. | ||||||||||||||
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19 |
Wed 3/24 | Sec 3.5 from the bottom of page 209 to the end (the Associativity subsection is recommended but not required). | Sec 3.5: 29, 37, 44, 47, 51, 53, 54. | ||||||||||||||
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18 |
Mon 3/22 | Sec 3.5 up to and including Example 5 part (a) (but not part (b)). | Sec 3.5: 1, 5, 9, 13, 17, 19, 21, 25. | ||||||||||||||
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17 |
Fri 3/12 | Sec 3.4 pages 191-197 up to but not including Theorem 10; skip the proof of Theorem 5. | Sec 3.4: 31, 35, 37, 41, 51, 52. EC: 53. Explain your work! |
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| Wed 3/10 | Covers HW 7-16, Sections 2.2-3.3 (except for skipped sections),
and Section 3.4 up to page 191. New: You should be able to prove the following theorems: Sec 3.2: Theorems 2e & 4. Sec 3.3: Theorems 2 & 4a-d. Sec 3.4: Theorem 3. |
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Mon 3/8 | Just review for the midterm. My suggestion on how to study for the midterm (like last time): For each section, first quickly review the definitions and main ideas, then do each HW problem in that section that you're not sure about. If you have to look at the book or your notes in order to do a problem, make sure to try that problem again a few hours or days later, with no book or notes. |
None. | ||||||||||||||
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16 |
Fri 3/5 | Sec 3.4 pages 187-191. | Sec 3.4: 7, 11, 13, 15, 17, 21, 25, 27, 29, 30. | ||||||||||||||
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15 |
Wed 3/3 | Sec 3.4 pages 179-186. Preview 187-189. | Sec 3.4: 1, 3, 5, 6, |
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14 |
Mon 3/1 | Finish Sec 3.3 up to but not including Example 10. | Sec 3.3: 35, 39, 43, 46, 47, 49. EC: 41. | ||||||||||||||
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13 |
Fri 2/27 | Sec 3.3 up to but not including Example 7. | Sec 3.3: 3, 11, 14, 15, 19, 23, 25. EC: Sec 3.2: 38, 42. |
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Wed 2/25 | Catch up and review. Then preview Sec 3.3. | |||||||||||||||
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12 |
Mon 2/23 | Sec 3.1 from Example 12; and Sec 3.2 (but skip Example 2). | Sec 3.1: 13, 17, 33, 39c. Sec 3.2: 7, 13, 21, 26, 27, 34. |
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11 |
Fri 2/20 | Sec 3.1 up to and including Example 9. | Sec 3.1: 1, 3, 5, 18, 19, 20, 21, 23, 24, 29, 30. | ||||||||||||||
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10 |
Wed 2/18 | Sec 2.3 pages 97-99. | Sec 2.3: 11, 20, 21, 25, 35, 42, 45. EC: 43. | ||||||||||||||
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9 |
Fri 2/13 | Sec 2.3 pages 89-97. | Sec 2.3: 1, 9, 13, 15, 18, 19, 22, 23. | ||||||||||||||
| Wed 2/11 | Midterm #1; covers Sections 1.1-2.1. Start reviewing this
weekend! My suggestion on how to study for the midterm: For each section, first quickly review the definitions and main ideas, then do each HW problem in that section that you're not sure about. If you have to look at the book or your notes in order to do a problem, make sure to try that problem again a few hours or days later, with no book or notes. |
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8 |
Mon 2/9 | Sec 2.2 pages 74, 78, 79. Preview 2.3. | Sec 2.2: 11, 21(1,3), 33, 35, 39, 45, 47. EC: 37 Explain your work! |
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7 |
Fri 2/6 | Sec 2.2 pages 67-77 but skip Theorem 1 and page 74 for now. | Sec 2.2: 1-9(odds), 16, 19, 23, 25. EC: 40 from Sec 1.3. |
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6 |
Wed 2/4 | Sec 2.1. Preview 2.2. | Sec 2.1: 1, 3, 11, 13, 15, 17, 23, 28, 29, 32, 34, 35. EC: 51 from Sec 1.2. |
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5 |
Mon 2/2 | Sec 1.3 pages 36-43. Skip 1.4 (at least for now). Preview 2.1. | Sec 1.3: 7, 13, 18c, 19c, 29, 33. Explain your work! (Please see bottom of page). |
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4 |
Fri 1/30 | Sec 1.3 pages 32-36. | Sec 1.3: 1, 5, 11, 15, 16, 28. | ||||||||||||||
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3 |
Wed 1/28 | Read rest of Sec 1.2. Preview 1.3. | Sec 1.2: 27, 37, 46, 52-54. | ||||||||||||||
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2 |
Mon 1/26 | Sec 1.2 up to projections (p.25). Preview rest of 1.2, and 1.3. Also read page xxv (before Section 1); it has some really good advice. |
Sec 1.2: 5,11,17,19, 23, 40, 42-44. EC: 50. | ||||||||||||||
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1 |
Fri 1/23 | 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," which will seriously hurt you later. |
Sec 1.1: 1d, 2d, 3c, 4c, 5a, 6, 9, 15, 17, 20, 23, 24. EC: 14abef (also find CD). |
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 interesting and sometimes more challenging; and may appear on exams only as extra credit problems (which carry no points).
Problems appearing in boldface should be turned in.
Explain your work: You should always explain your work, even if the book doesn't ask you to. How much should you explain? Pretend you're explaining it to a classmate who doesn't know how to do the problem.