Math 104.01 (Linear Algebra)

Spring 1999

Plan for Week 7

This week we have a take-home test on Chapters 1 and 2. On Monday we will work in groups on sample problems of a type that might occur on a take-home test. The test will be handed out at the end of class on Wednesday and will be due at the start of lab on Friday.

The rest of this week and the remaining two weeks before Spring Break, we will cover most of Chapter 4, which your author describes in the following words (p. 210, emphasis added):

"The mathematical seeds planted in Chapters 1 and 2 germinate and begin to blossom in this chapter. The beauty and power of linear algebra will be seen more clearly when we view [the space of real n-vectors] as only one of a variety of vector spaces that arise naturally in applied problems. We will find that a study of vector spaces is not much different from a study of [the space of n-dimensional vectors] itself, becasue we can use our geometric experience with [the plane] and [3-space] to visualize many concepts.

We start our study of Chapter 4 with basic concepts about vector spaces and subspaces, including connections with our prior study of matrices and linear transformations. It's very important that we see this Chapter as a nearly-three-week-long unit that will reveal the flowering described above.

To see the syllabus for Week 7 in a separate window, click here.

1. Your next homework papers will be turned in on Monday, March 1. Those papers should include solutions to all problems from the textbook in the assignment below -- but not the practice problems for the test. The assignment dates are start dates.
2. In general, no solution will be given full credit unless you have written an explanation of why you know it is correct. (Exceptions to this rule are the exercises whose numbers appear in parentheses.)
3. This week's lab is related more to past work than to this week's subject. We will explore the properties of the linear transformations that have the effect of rotating all the vectors in their domain through a fixed angle. Among other things, we will see that such transformations are rather special from the point of view of determinants.

Assignments

• Monday, Feb. 22, practice problems to be distributed in class
• Wednesday, Feb. 24, Sec. 4.1 / #1, 2, 4, 7, 8, 9, 11, 12, 13, 19, 20, 21, 22, 23, 24, 31, 33, 35
• Friday, Feb. 26, Sec. 4.2 / #1, 3, 7, 11, 14, (17), (18), 21, 23, 25, 26, 31, 33, 34, 39, 40

Last modified: February 11, 1999