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!
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 for a classmate who doesn't know how to do the problem to be able to follow and understand your work.
Reminder: 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. Okay?
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HW # |
Due | Read | Do |
|---|---|---|---|
| F 12/9 1:00-4:00 PM F 12/9 Fowler 307 |
Cumulative, with emphasis on HWs 25-29. For practice, here's last year's final exam. |
Just for fun: Play the game Lights
On (but only after you're done with all your finals!), and take a
look at Sec 2.4 Example 2.33. |
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|
29 |
M 12/5 | Read Sec 7.3 up to and including Example 7.28; may skip proofs of Theorems 7.8 and 7.9. |
Sec 7.3: 1, 7, 15. Optional: do these additional problems (click). |
|
28 |
F 12/2 | Read Sec 5.3 up to but not including ``The QR factorization''; may skip the proof of Theorem 5.15. |
Sec 5.3: 1, 7, 11. Sec 5.2: 28, 29. Also do these additional problems (click). |
|
27 |
W 11/30 | Read the rest of Sec 5.2: Orthogonal
Projections. Learn the proof of Theorem 5.9. |
Sec 5.2: 17, 21, 27. Also do these additional problems (click). |
|
26 |
M 11/28 | Read Sec 5.2 up to but not including the subsection Orthogonal Projections. Learn the proof of "row(A)^perp = null(A)" (the proof that we did in class). | Sec 5.2: 1, 3, 5, 11, 23-26. |
|
25 |
M 11/21 | Read Sec 5.1 up to but not including the subsection Orthogonal Matrices. Also read and learn the proofs of Theorems 5.1-5.3. |
Sec 5.1: 1, 3, 7, 11, 12. Also do these additional problems (click). |
| W 11/16 | Covers HW 17-24, and their corresponding sections. For practice, here's last year's Midterm #3. |
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|
24 |
M 11/14 | Read Sec 4.4. up to but not including Theorem4.24. Also read Example 4.29, and the proofs of Theorems 4.21-4.23. | Sec 4.4: 1, 3, 5, 7, 9, 19, 30, 31, 32, 33. |
|
23 |
W 11/9 | Read Sec 4.3. Learn the proofs of Theorems 4.15 and 4.18. | Sec 4.3: 5, 13, 14, 15, 16, 19, 22, 24, 25. |
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22 |
M 11/7 | Read the rest Sec 4.2 up to but not including Cramer's Rule and the
Adjoint. Also read the Exploration section on Cross Products (between Sections 1.3 and 1.4). |
Sec 4.2: 42, 44, 49, 50, 51, 53, 54. Page 46: 3, 4b, 5abcdef (hint: use properties of determinants). Also, prove that A is singular iff det(A)=0 by completing the proof outline given in class (don't need to turn this in). |
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21 |
F 11/4 | Sec 4.2, up to but not including Determinants of Elementary Matrices. | Sec 4.2: 3, 13, 15, 17, 19, 20, 30, 33, 39, 40. |
|
20 |
W 11/2 | Sec 4.1 (skip the last two examples). |
Sec 4.1: 3, 7, 13, 17, 19, 21, 22, 23. Also turn in the following problem: Let lambda be an eigenvalue of an n x n matrix A. Prove that the set of all eigenvectors of A corresponding to lambda is a subspace of R^n. |
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19 |
M 10/31 | Read the rest of Sec3.6. | Sec 3.6: 29, 38, 44, 47, 49, 53, 54. |
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18 |
F 10/28 | Sec 3.6 up to and including Example 3.59 part (a) (but not part (b)). | Sec 3.6: 1, 5, 9, 13, 17, 19, 21, 25. |
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17 |
W 10/26 | The rest of Sec 3.5, except for the subsection Coordinates. |
Sec 3.5: 17, 18, 21, 25, 27, 40, 45, 48 (hint:
add them), 55, 56, 57ab, 58, 59ab. (Note:
part (a) of 57 and 59 are boldface.) |
| W 10/19 | Covers HW 7-16 and Sections 2.1-3.5 (except for skipped
material). For practice, here's last year's Midterm #2. |
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|
16 |
W 10/12 | Sec 3.5 from Theorem 3.21 up to and including Theorem 3.24. | Sec 3.5: 15, 34, 39. May use calculator or web tools to find rref. |
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15 |
M 10/10 | Sec 3.5 up to and including Theorem 3.20. | Sec 3.5: 1, 2, 3, 5, 6, 7, 10, 11, 13. |
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14 |
F 10/07 | The rest of Sec 3.3. | Sec 3.3: 35, 39, 43, 46, 47, 49, 56. |
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13 |
W 10/05 | Sec 3.3 up to but not including the Fundamental Theorem of Invertible Matrices. | Sec 3.3: 3, 11, 14, 15, 19, 22, 23, 25, 30. |
|
12 |
M 10/03 | Sec 3.1 from Example 3.12. Sec 3.2 (but skip Examples 3.16-3.18). |
Sec 3.1: 13, 17, 33, 39c. Sec 3.2: [7, 13 Optional], 26, 27, 30b, 34, 35, 36. |
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11 |
F 9/30 | Sec 3.1 up to and including Partitioned Matrices | Sec 3.1: 1, 3, 5, 18, 19, 20, 21, 23, 24, 29, 30. Turn in all evens. |
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10 |
W 9/28 | Read the rest of Sec 2.3. | Both editions: Sec 2.3: 11, 20, 21, 25, 27, 35, 37, 42, 45. |
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9 |
M 9/26 | Read Sec 2.3 up to but not including "Linear Independence". | Both editions: Sec 2.3: 1, 9, 10, 13, 15, 18, 19, |
|
8 |
F 9/23 | Read about "Rank" and "Homogeneous Systems" in
Sec 2.2; may skip "Linear Systems over Zp. Preview
Section 2.3. Check out this great webpage: http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi |
2nd ed: Sec 2.2: 11, 23(1,3), 35, 37, 41, 47, 49. EC: 39. 1st ed: Sec 2.2: 11, 21(1,3), 33, 35, 39, 45, 47. EC: 37 |
| W 9/21 | Covers HWs 1-6 and Sections 1.1-1.3 and 2.1. Start reviewing
now! My suggestion for 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. Last year's Midterm #1. |
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|
7 |
M 9/19 | Sec 2.2, but skip "Rank" and "Homogeneous systems" for now. | 2nd ed: Sec 2.2: 1-9(odds), 16, 19, 25, 27. 1st ed: Sec 2.2: 1-9(odds), 16, 19, 23, 25. |
|
6 |
F 9/16 | Sec 2.1. | Sec 2.1: 1, 3, 11, 13, 15, 17, 23, 28, 29, 32, 34, 35. |
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5 |
W 9/14 | Read the rest of Sec 1.3. | 2nd and 1st ed: Sec 1.3: 7, 13, 18c, 19c, 29, 33. Remember: you must always explain your work, even if the book doesn't ask for it. How much detail should you include? See the note above this table. |
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4 |
M 9/12 | Read Sec 1.3 up to "Planes in R^3." | 2nd and 1st ed: Sec 1.3: 1, 5, 11, 15, 16, 28. |
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3 |
F 9/9 | Read rest of Sec 1.2. Preview 1.3. | Sec 1.2: 31, 41, 54, 62-64. 1st Ed: Sec 1.2: 27, 37, 46, 52-54. |
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2 |
W 9/7 | Sec 1.2 up to projections (p.25). Preview rest of 1.2, and 1.3. Also read page xxiii (xxv in 1st Ed) (before Section 1); it has some really good advice. |
2nd Edition: Sec 1.2: 5,11,17,19, 25, 44, 47, 48, 52. EC: 58. 1st Edition: Sec 1.2: 5,11,17,19, 23, 40, 42-44. EC: 50. |
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1 |
F 9/2 | 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: 14 (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. Work on them only if and when you have mastered all the other problems.