M340L Homework

Homework Assignments for
M340L, Applied Linear Algebra

This page is always under construction, so you should check it regularly. Assignments with the due date in bold face are set in stone. Other assignments are still tentative.

The homework is due every Thursday in lecture, except for the first week. The assignments will appear on this page.

Late homework will not be accepted, even a few minutes after class is over, unless you are sick or have made prior arrangements with me. In other words, you must attend class!

Each written homework will be graded on a 10-point scale. Some of those points will be for completing all of the problems. Some are for the accuracy of your solution to one or two selected problems. (Our grader is only working 5 hours/week.)

You are encouraged to work homework in groups, since the best way to learn something is to explain it to somebody else! (If you still don't understand, come to Mark and me for help -- don't pay good money for bad tutoring when you can see the professor and TA for free.) However, each person should turn in his own homework, and you should only submit what you have calculated yourself (possibly with help). Working together is fine; mindless copying is not; respecting the difference is a matter of honor and integrity. At the end of the semester I will drop one homework score, and average the rest.

The homework is in two parts. There are the required problems, which you need to turn in, and the suggested problems, which are for practice and further learning.

Thursday, January 19 First week. No homework due.

Thursday, January 26
Section 1.1: Required: 6, 9, 25; Suggested: 1, 4, 15, 19, 31
Section 1.2: Required: 3, 7c, 28; Suggested: 1, 2, 4
Section 1.3: Required: 2, 3, 8; Suggested: 4, 6, 10

Thursday, February 2
Section 2.1: Required: 12, 16; Suggested: 1, 2, 3, 5
Section 2.2: Required: 11, 12, 23; Suggested: 1, 2, 5, 27
Section 2.3: Required: 16, 25, 26; Suggested: 1, 3, 4, 12
Section 2.4: Required: 1, 2, 6; Suggested: 11, 14, 20, 22

Thursday, February 9
Section 2.5: Required: 6, 22, 27, 29; Suggested: 5, 21, 23, 34. (On 34, you can assume that A and D are invertible)
Section 2.6: Required: 1, 2, 3, 4; Suggested: 7, 16, 17.

Thursday, February 16 Section 2.7: Required: 3, 6, 7, 9, 17, 18; Suggested: 1, 2, 11, 13, 19.

Thursday, February 23
Section 3.1: Required: 10, 11, 17, 19, 23, 27; Suggested: 12, 14, 15, 18, 20
Section 3.2: Required: 1,2,3,4,22; Suggested: 9, 13, 14, 21.

Thursday, March 1
Section 3.3: Required: 2, 6, 8, 24; Suggested: 1, 7, 11
Section 3.4: Required: 1, 4, 6, 10; Suggested: 2, 3, 13.
Section 3.5: Required: 1, 9 ,11, 16; Suggested: 2, 12, 20, 23.

Thursday, March 8
Section 3.6: Required: 2, 5, 7, 28; Suggested: 1, 13, 14, 23.
Section 4.1: Required: 3, 9, 19, 22. Suggested: 4, 11, 13.
Section 4.2: Required: 5, 8, 11, 17; Suggested: 2, 13, 16.

Thursday, March 15 Spring break. No homework due.

Thursday, March 22
Section 4.3: Required: 1-4, Suggested: 5-7
Section 4.4: Required: 16, 18, 21; Suggested: 13, 15

Thursday, March 29 Section 5.1: 1-7, 9, 12 (all required)

Thursday, April 5
Section 6.1, # 1, 4, 6, 21 (required) and 2, 3, 5, 19 (suggested)
Section 6.2, #6, 7, 12, 18 (required) and 1, 13, 25 (suggested)

Thursday, April 12 Section 6.3 # 1, 4, 6, 8, 9; Section 6.4 #2, 3, 4; Section 8.3 #1, 2
All these are required. Instead of working optional problems, read sections 6.1-6.4 and 8.3 VERY thoroughly in preparation for the midterm. There's a lot of important material there! However, you can skip the "second order equations" and "stability of 2x2" parts of 6.3, the "eigenvalues versus pivots" part of 6.4 and the economics part of 8.3. These sub-sections will not appear on the exam.

Thursday, April 19 Section 6.4, #7, 9. Section 6.5 #1, 2, 6 (all required)

Thursday, April 26 Section 7.1, #3, 4, 6, 11, 12; Section 7.2 # 1, 2, 5, 6, 7

Thursday, May 3 Section 7.2, #13, 14, 18, 20, 21, 24, 32
Also, do the following two problems:
1) Let V=W be the space of quadratic polynomials in a variable t. Let L:V => W be a linear transformation that shifts the graph of a polynomial one unit to the right. That is, if x(t) is a polynomial, Lx(t) = x(t-1). Find the matrix of L with respect to the standard bases for V and W (namely {1,t,t²} )
2) Let V=W be the space of 2x2 matrices, and let L: V => W be the transpose operation: If x is a 2x2 matrix, then L(x)=x^T. Pick a basis for V (and W) and find the matrix of L with respect to that basis. There's more than one possible answer, since there's more than one possible basis, but the simplest answer is pretty clear.