I will be conducting shared office hours with two other instructors of Math 308 this quarter. Think of it as a "mini Math Study Center" just for linear algebra. I highly encourage you to use these hours to come and work with other students on homework, do your reading, etc. even if you do not need help from an instructor. These office hours will take place in the Art building, room 334, at the following times:
- Tuesdays 2-4 and 4:30-5:30 [NOTE CHANGE],
- Thursdays 12:30-2:30.
- Homework assignment 1 -- Due Monday, Jan 10:
- 1.1: 17, 20, 22, 29, 32
- 1.2: 10, 16, 18, 21, 31, 35, 39, 41, 45, 49, 50
- 1.3: 4, 12, 18, 23, 24, 33 [Hint: write one equation for each of the three points.]
- Homework assignment 2 -- Due Wednesday, Jan 19:
- 1.5: 4, 9, 13, 18, 21, 31, 45, 46, 52, 55, 57, 62, 68
- 1.6: 7, 13, 17, 19, 26, 43, 47
- 1.7: 1, 2, 6, 12, 24
- Homework assignment 3 -- Due Wednesday, Jan 26:
- 1.7: 46, 47, 49, 52
- 1.8: 2, 9, 27
- 1.9: 2, 5, 9, 15, 39, 50, 51, 56*, 58, 69
*To problem 56, add the following part (b). We will investigate how this matrix behaves in the case where n=2 using the following example. Let v=
and find A. Draw a set of 2d coordinate axes, and graph the vector v and the line y=-x. Using the vectors 
, graph each of v, Av, w1, Aw1, w2, Aw2, w3, Aw3 on the same set of axes. Then describe in words what you think multiplation by A does to vectors.
[Answer to 56(b): the effect of A is to reflect all vectors across the line y=-x, which is the line perpendicular to v. In R^3, the effect of such a matrix (from part a) is to reflect vectors across the plane perpendicular to v. Etc.]
- Homework assignment 4 -- Due Wednesday, Feb 2:
- 3.1: 13, 16, 25
- 3.2: 1, 2, 3, (5)*, (8), (10), 11, 17, 18, 20, (27), 28, 29
*Questions in parentheses do not need to be turned in. - 3.3: 3, 5, 6, 23, 33, 44, 50
- Homework assignment -- not collected:
- 3.4: 1, 5, 9, 11, 29, 30, 36, 37
- Homework assignment 5 -- Due Wednesday, Feb 16:
- 3.5: 1, 4, 5, 11, 15, 19, 22, 25, 29, 33, 38, 41
- 3.6: 1, 5, 9, 13, 23, 28, A*
*Problem A: Consider the matrix
.
Find orthonormal bases for the kernel and range. (Notice: that says orthonormal, not merely orthogonal.)
- Homework assignment 6 -- Due Wednesday, Feb 23:
- 3.7: 4, 5, 9, 13, 17, 18, 19*, 26**, 30, 32, 46
*Hint: [1 1]^T = e_1 + e_2, and T(e_1+e_2) = T(e_1)+T(e_2).
**The kernel and range of T are just the kernel and range of the representing matrix A. Same with rank and nullity (dim Ker A). - 3.9: 11 - 14.
[I would actually recommend finding orthonormal bases for the two subspaces ahead of time.]
- 3.7: 4, 5, 9, 13, 17, 18, 19*, 26**, 30, 32, 46
- Homework assignment 7 -- Due Wednesday, Mar 2:
- 3.8: 1, 2, 7, 12, 17*
*The point of this is that it shows least-squares polynomial fits to data are always unique. - 4.2: 1-4, 7, 8-11, 17, 18, 21, 24, 25, 26, 27, 28
- 3.8: 1, 2, 7, 12, 17*
- Homework assignment 8 -- Due Wednesday, Mar 9:
- 4.1: (17)*, 18
- 4.3: 1, 3, 7, 13, 14, 18, 21, (23), 25, 28
- 4.4: 1, 3, 5, 6, (8), 14, 30
- 4.5: 1, 3, 10, 11, 13, 14, (22)
*Questions in parentheses do not need to be turned in.
- Homework assignment 9 -- not collected:
- 4.7: 1, 5, 11
- 4.8: 3, 9*, 23, (24), (25)
*Also find the eigenspace E1.
- Friday, Jan. 7 -- Quiz 1. May be taken starting after class, and ending at midnight.
- Friday, Jan. 14 -- Quiz 2. May be taken starting after class, and ending at midnight.
- Saturday, Jan. 22 -- Quiz 3. May be taken anytime on Saturday (midnight to midnight).
- Saturday, Jan. 29 -- Quiz 4.
- Saturday,Feb. 5 -- Quiz 5.
- Saturday, Feb. 12 -- Quiz 6.
- Saturday, Feb. 19 -- Quiz 7.
- Saturday, Feb. 26 -- Quiz 8.
- Saturday, Mar. 5 -- Quiz 9.
- Friday, Jan. 7 -- Worksheet 1 (Network Flow)
- Friday, Jan. 21 --
Worksheet 2 (Polynomial Interpolation)
Solutions to Worksheet 2 - Wednesday, Feb. 16 -- Worksheet 3 (Linear Transformations)
- Monday, February 7, in lecture. The exam will cover all class material up to section 3.4 (bases for subspaces). It will be 50 minutes. You may bring a scientific calculator (not graphing). You may bring an 8.5x11 double-sided sheet of notes for use during the exam, handwritten by you.
- Some Math 308 midterms from previous quarters (courtesy of Lindsay Erickson). Also Paul Smith's course webpage has some excellent practice midterms (unfortunately with inline answers, so you have to cover them up).
- Midterm (blank)
- Midterm with answers
- Monday, March 14, 2011, 2:30-4:20 pm, in Bagley 261 (our usual classroom)
- Same rules as the midterm. It will be one hour and 50 minutes long. You may bring a scientific calculator (not graphing). No electronic devices can be used during the test, with the exception of your scientific calculator. You may bring an 8.5x11 double-sided sheet of notes for use during the exam, handwritten by you.
- Includes all topics covered in class. Sections covered since the midterm exam may be represented more heavily, however.
- The format will be similar to the midterm, though longer, with some fill-in-the-blank or true-false questions, some computation questions, and some proof questions (expect slightly more involved proofs, since there is more time).
- Some practice finals from previous quarters (courtesy of Lindsay Erickson). Also Paul Smith's course webpage has two great practice finals, which should be useful in testing your knowledge (although the format is different from our exams). Another very useful study resource is the "conceptual exercises" sections at the end of each chapter in our textbook.
- Review outline from the last two days of lecture, listing the main ideas we've discussed in class.