Math 232 Reading and Homework
The
starred problems are the ones designated for grading.
|
Number |
Assignment |
Due |
|
1
|
(1)
Read the Course Information and Syllabus page and familiarize yourself with
the course homepage. |
Wed,
Sept 17 |
|
2
|
(1)
Read 1.2 |
Fri,
Sept 19 |
| 3 | (1) Read 1.3 and the handout "What's In a Name?"
(2) Check out this nice introduction to Mathematica. (3) page 35: 5, 13, 23, 25, 29 (see page 9 for the definition of a diagonal matrix), 33, 34*, 37*, 49, 55 (4) On pages 36-37, do 38-43 using Mathematica. Write one or two paragraphs (and turn it in with your regular homework) summarizing your results. In Mathematica,, the command A = Table[ Random[ ], {3}, {3} ] will generate a 3x3 matrix of random numbers, and A = Table[ Random[ ], {3}, {4} ] will generate a 3x4 matrix, etc. To display this in matrix form then type A // MatrixForm. To row-reduce your matrix, type RowReduce[A] // MatrixForm. (Note that this in this exercise you are generating coefficient matrices and not augmented coefficient matrices.) (5) The True or False questions at the end of each chapter are an excellent way to study concepts. Note that to show a statement is true you need to give a convincing explanation. To show that a statement is false you only need to give one counter-example. Here are the solutions to the True-False questions in Chapter 1 for your self-study: TFFTT FFFTT FFTTT TTTFF FTFTF TFFFT TTFTF TTTFF TTTFT. (6) If you would like your own copy of Mathematica you can download the installation by going to Collab -> Departments -> MATH -> MathematicaInstallers. If you have any questions, contact Mike Tie, the math department's Technical Associate, at x4067. | Mon, Sept 22 |
| 4 | (1) Read 2.1
(2) p 51: 5, 17, 19, 21, 23, 42*, 44*, 45, 47, 49*; page 38: 57 (3) Reminder: Quiz #1 next Monday. |
Wed, Sept 24 |
| 5 | (1) Read 2.2 and 2.4 (skim over invertibility; we'll cover that on Friday)
(2) p 66: 7, 14, 19, 21*, 27, 37, 42; page 89: 13, 14, 16, 17, 28, 29, 77* |
Fri, Sept 26 |
| 6 | (1) Read 2.3 and review Chapter 2. (Make sure to also read about partitioned matrices, which were not
covered in class.)
(2) p 76: 10 (Check your answer), 29*, 35, 45, 46, 53*, 54*; p 89: 19, 21, 23*, 25, 43 (think geometrically), 65, 71 (3) Challenge page 93: 84 (4) Here are the solutions to the True-False questions in Chapter 2: TFTTF TFFTT FTTTF TFTFT FTFTT TTFFT FFTTT TFTFT TFTFT TFFFF FTTFTT. (5) Reminder: The first quiz is on Wednesday. It will cover Chapters 1 and 2. | Mon, Sept 29 |
| 7 | (1) Read 3.1
(2) p 109: 5, 13, 16, 19, 23, 33, 35, 37*, 40, 44* (If either of the statements are true, you need to give a convincing explanation; if either of the statements are false, give a counter-example.) (3) Also to be turned in: Let A be a 4 by 3 matrix with rows {1,2,1}, {1,2,2}, {1,2,3}, and {1,2,4}. Find the kernel and image of A, expressing both sets as the span of a set of vectors. Give as few vectors as possible. (4) Extra Credit Challenge page 111: 53, 54. (To receive extra credit turn these problems in separately from your homework with a nice write-up. You may turn this in on Friday.) | Wed, Oct 1 |
| 8 | (1) Read 3.2
(2) p 121: 1, 2*, 3, 4*, 5, 53* |
Fri, Oct 3 |
| 9 | (1) Reread 3.1 and 3.2 and read the Markov chain handout
(2) page 121: 19, 25, 29, 33*, 34, 42, 43, 46*, 55* (3) Also to be turned in from the Markov Chain handout: Exercises 1, 3(b), 7, 8 (For these problems, whenever you solve for the steady-state vectors do it exactly as in the examples on pages 595-596.) (4) Challenge page 122: 36, 37 | Mon, Oct 6 |
| 10 | (1) Read 3.3
(2) page 133: 15, 17, 23*, 29, 31*, 35, 36*, 37, 39* (3) Challenge page 135: 61 (4) For the True-False questions at the end of Chapter 3 ignore the questions that contain the word "similar," as this relates to material in Section 3.4, which we will cover later in the term. Here are the solutions to the True-False questions: FTTFT FTFTF TTFTT FTTTT FFTTT TFFTT TFFFF TTFFT TFTTT TTFTT FTF | Wed,, Oct 8 |
| 11 | (1) Read 5.1 (But you can skip the sections we did not cover in class.)
(2) page 198: 3, 5, 11*, 29*, 41, 43* (3) Find some real data on two quantitative variables that seem related. (Check out an almanac, the internet or the library.) Compute their correlation. Show your work and include the data. (4) Challenge page 200: 20 (5) Reminder: Test #1 on Monday (Chapters 1, 2, 3 (except 3.4), and Markov Chains) | Fri, Oct 10 |
| 13 | (1) Review 5.1
(2) page 201: 17*, 27, 28*, 29, 37 (3) Challenge page 200: 18, 35, 36 (The last two problems use the Cauchy-Schwarz inequality.) | Wed, Oct 15 |
| 14 | (1) Read 5.3 and skim 5.4
(2) page 216: 11, 18, 19, 21, 23, 32(a)* (Exhibit a counter-example to show that this is false; note that (b) is true.), 35*, 39, 40* (see below), 44* (3) See Fact 5.4.7 on page 223. Use this to answer 40 on page 217. One could also use Fact 5.3.10 to obtain this projection matrix as follows. I claim that { [ 1/2, 1/2, 1/2, 1/2 ], [ -1/10, 7/10, -7/10, 1/10 ] } is an orthonormal basis for the subspace W. Now use Fact 5.3.10 to obtain the projection matrix. Finally, show that this basis is in fact a basis for W. (The vectors are clearly linearly independent; one must show that they span W.) | Fri, Oct 17 |
| 15 | (1) Read Section 5.4.
(2) Do the following problems by hand. Page 228: 2*, 4, 19, 21*, 25 (3) Do the following problems using Mathematica. Refer to the Least Squares notebook (on the Handouts page). Include your Mathematica output with your work, but write up your solutions separately and clearly: Page 231: 39*, 40* (The reference to Kepler's laws of planetary motion is referring to Kepler's Third Law. Google this if you need to. (4) Start studying the True-False questions at the end of Chapter 5. The relevant questions are 1-13, 15, 17-28, 30-34, 36-41. Here are the solutions to all the True-False questions in Chapter 5: TFTTF TFTFT TTFTF TTFFF TTFTF TTFFT FTTTF FTTTF TTTTT TTFFT. | Wed, Oct 22 |
| 16 | (1) Read 6.1 and 6.2. In 6.1, ignore Sarrus's Rule and anything involving mathematical induction.
In 6.2, read page 261 to the middle of page 266. The rest is
optional.
(2) 6.1, page 259: 9, 15, 21, 41, 59; 6.2, page 271: 30*, 37 (Hint: Use Fact 6.2.4), 38, 40*, 41, 45*, 48* (3) Reminder: Quiz #2 is on Monday. |
Fri, Oct 24 |
| 17 | (1) Read pp 297-299 in 7.1 and all of 7.2.
(2) page 302: 1, 3, 9, 15, 17, 19; page 314: 1, 11, 15, 33 (Nothing needs to be turned in for Monday.) (3) Reminder: Quiz #2 is on Monday and will cover material from Chapters 5 and 6. | Mon, Oct 27 |
| 17 | (1) Read 7.3
(2) Turn this in with your homework: Let A be a general 2x2 matrix. (Label the entries a, b, c and d.) Find the eigenvalues of A (in terms of a, b, c, and d). Now show that the determinant of A is equal to the product of the eigenvalues. Also show that the trace of A (defined as the sum of the diagonal entries) is equal to the sum of the eigenvalues. This property holds for all square matrices: the determinant is equal to the product of the eigenvalues (counting their multiplicities) and the trace is equal to the sum of the eigenvalues. (3) For each of the matrices in the following problems, give all the eigenvalues along with their eigenspaces. Find a basis for each eigenspace. Give the algebraic and geometric multiplicy of each eigenvalue. If an eigenbasis exists, find it. page 324: 1*, 5, 9, 13*, 21, 27, 41* | Wed, Oct 29 |
| 18 | (1) Read 7.4 starting at the top of page 330 to the bottom of page 334. (Ignore references to
"coordinates" and "similarity"; these will be discussed on Friday.)
(2) page 326: 39(b), 44*, 46*; page 338: 3, 6*, 8*, 31 (3) Happy Halloween! | Fri, Oct 31 |
| 19 | (1) Read 3.4.
(2) page 146: 21, 24*, 27, 37, 41*, 59, 67, 74* (3) Challenge If A and B are similar matrices show that they have the same nullity and the same rank. | Mon, Nov 3 |
| 20 | (1) Read 8.1 and 8.2 You may skip the material on pp 375-376 on "definiteness."
(2) page 370: 3, 10*, 12*, 29*; page 378: 3, 18*, 24, 25 (3) Reminder: Midterm exam is Monday, Nov. 10 | Wed, Nov 5 |
| 21 | (1) Read 4.1. This section is very important and should be read carefully.
(2) True-False questions. For Chapter 3, now that we've covered Section 3.4 you can study all of the T/F questions in that chapter (see solutions, above). For Chapter 6, relevant questions are: 1-16, 18-20, 22-25, 31-33,38-40. Here are all solutions for Chapter 6: TTTFF TFFTT TFTFT FTFTT TTFFT FFTFT FFFTT TTFFF TFTTT TF. For Chapter 7, relevant questions are: 1-6, 9-14, 18-22, 24-41, 43-57. Solutions for Chapter 7: TTFTT TTFTT FFTTT FTTTF FTFFT FTFFT FTFFF TTTTT FTFTT TTFTF TFTTT TTT. For Chapter 8, relevant questions are: 1, 3, 5, 8, 10-12, 14, 16, 19, 21, 24-27, 37, 40. Solutions for Chpater 8: TTFTF FTTTF FTTTF FTTTF FTTTF TTFTT FTFTT TFTFT TFFTT TFTFF TTT. (3) No homework for Friday. | Fri, Nov 7 |
| 22 | (1) Review for Midterm #2
(2) No homework for Monday. (3) I will post some homework which won't be due until Wednesday, Nov 12. | Mon, Nov 10 |
| 23 | (1) This week's reading: 4.1, 4.2, and 4.3 (up until bottom of page 175--we will not cover "Change of
Basis").
(2) page 162: 3, 7, 11, 13, 29; For the exercises from Section 4.2, determine (i) whether or not the transformation is linear; (ii) find the kernel and image; (iii) find the nullity and rank. Page 169: (6 and 52)*, (13 and 51), (25 and 53)*, 33; page 180: 14*, 33* (3) Challenge Page 163: 58; page 171: 78 | Wed, Nov 12 |
| 24 | (1) Continue reviewing Chapter 4 (all of the material except Chapter 4)
(2) page 180: 1, 3, 6*, 7*, 27, 33, 49, 55, 57*, 59, 64, 66*, 68* (3) Here are the solutions to the True/False questions in Chapter 4: TTFTT TTFTT FTFFF TFFFT TTTTF TTTFT FFFTT TTTFT TFTFT FTFFT TFTTT TTFTF TFTFT FT. You can ignore all questions involving (i) infinite-dimensional subspaces and (ii) change of basis. (4) Reminder: Quiz #3 (covering Chapter 4) is Monday. | Fri, Nov 14 |
| 25 | (1) No homework for Monday. Study for Quiz #3 (Chapter 4) | Mon, Nov 17 |
| 26 | (1) Read 5.5
(2) page 243: 9, 12, 20, 26, 27, 28, 29 (3) Final Exam is Saturday, Nov 22, 8:30-11 am. |
Wed, Nov 19 |
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