** Note: ** My office hours have changed, as of mid-October. They are: Monday 12-1, Tuesday 1-2, Friday 10-11.

Reading: Sections 1.1, 1.2

Section 1.1: 2, 4, 12, 18, 20, 22, 32, 33

Section 1.2: 2, 4, 8, 10, 12, 16, 26, 28

Reading: Section 1.3, and page 52-53 of Section 1.6

Section 1.3: 2, 4, 8, 10, 12, 22, 26, 29, 30, 32

Section 1.6: 12, 14

Problem 1: Let ** u ** be the vector [1, 0, -1, 3] and ** v ** be the vector [3, 2, -5, 9]. (My html skillz are poor... those should be columns of course.)

a) Consider the general vector **a** = [w, x, y, z] in **R**^{4}. Find equations in w, x, y, and z which determine when **a** is in the span of **u** and **v**.

b) Is the vector **b** = [1, 1, 2, 3] in the span of ** u ** and ** v **? If so, express **b** as a linear combination of ** u ** and ** v** (i.e. find the coefficients).

c) Is the vector **c** = [-2, 2, 0, -6] in the span ** u ** and ** v **? If so, express **b** as a linear combination of ** u ** and ** v** (i.e. find the coefficients).

(**Hint**: after finishing part (a), parts (b) and (c) should be doable without any more row reduction.)

Here is Practice Midterm 1. Give yourself 50 minutes and see how you do. Solutions will be posted by Friday. The midterm roughly covers sections 1.1 through 1.4, and part of 1.6. Here are the solutions.

Reading: Sections 1.4, 1.5

Section 1.4: 2, 4, 14, 16, 20, 22, 24, 32, 36

Section 1.5: 4, 6, 8, 12, 16

Reading: Sections 1.7, 2.8

Section 1.5: 10, 18, 20, 22, 26, 28, 30, 32

Section 1.7: 2, 4, 6, 8, 10, 22

Section 2.8: 2, 4, 8, 10, 12

Reading: Section 2.9

Section 1.7: 18, 20, 24, 26, 28

Section 2.8: 16, 18, 20, 22

Section 2.9: 2, 4, 6, 8, 10, 12, 14, 16, 20

I've been going a little fast, but I will slow down in preparation for the next midterm. Nonetheless, I recommend doing these problems sooner rather than later, while the material is fresh.

Reading: Section 1.8, 1.9, 2.1, and the part of 1.10 about difference equations.

Section 1.8: 8, 12, 18, 20, 22

Section 1.9: 2, 6, 10, 14, 24, 26 (whenever you see the word "one-to-one," you should replace it with the word "injective." The book defines "one-to-one" to mean what I mean when I say "injective," but I had a different meaning for "one-to-one").

Section 1.10: 10

Section 2.1: 2, 8, 10, 12, 20

Here is Practice Midterm 2. Give yourself 50 minutes and see how you do. There is a bonus word problem, to give you additional flavors of word problem, but it should not be counted for timing purposes. Solutions are now posted. The midterm roughly covers sections 1.5, 1.7 through 1.9, 2.1, and 2.7 through 2.9. The first page of the practice midterm gives a rough list of topics.

Reading: Section 2.2, 2.3.

Section 2.1: 22, 24, 26

Section 2.2: 2, 4, 8, 10, 32, 35, 38

Section 2.3: 2, 4, 6, 8

Reading: Section 3.1, 3.2.

Section 2.3: 12, 14, 20, 26

Section 3.1: 2, 6, 12, 14, 16, 18

Section 3.2: 22, 26

Reading: Section 3.3.

Section 3.2: 8, 12, 28, 36, 40

Section 3.3: 2, 6, 12, 20, 24, 28

Here is a Quasi Practice Final. It is not intended to be the length of the final, and it encapsulates only the material since Midterm 2. The actual final will be comprehensive. I thought it was more worthwhile to give more examples of the fresh material. I also included a list of topics. Solutions are here.

The final will cover Ch 1.1 - 1.10 (network flows from 1.6, difference equations from 1.10), Ch 2.1 - 2.3 and 2.8 - 2.9, Ch 3.1 - 3.3, and Ch 4.1 - 4.6.Ben Elias

Department of Mathematics

Fenton Hall, Room 210

University of Oregon

Eugene, OR 97403

Phone: (541) 346-5629

Fax: (541) 346-0987

e-mail: bezzzzlizzzzas@uorezzzzgon.edu