Math 104.01 (Linear Algebra)

Spring 1999

Plan for Week 9

This is our third and final week on Chapter 4, the central unit in the course. Again we quote the text (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 Rⁿ 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 Rⁿ itself, because we can use our geometric experience with R² and R³ to visualize many concepts.

"Beginning with basic definitions in Section 4.1, the general vector space framework develops gradually throughout the chapter. A goal of Sections 4.3-4.5 is to demonstrate how closely other vector spaces resemble Rⁿ. Section 4.6 on rank is one of the high points of the chapter, using vector space terminology to tie together important facts about rectangular matrices. ..."

Our lab at the end of the week is on an important application (Markov chains) that has already made a couple of appearances earlier in the course. After Spring Break we will use this topic as a lead-in to the next chapter.

To see the syllabus for Week 9 in a separate window, click here.

1. Your next homework papers will be turned in after Spring Break on Monday, March 22. Those papers should include solutions to all problems in the assignment below. The assignment dates are start dates, but you can start on the problems in Sec. 4.9 before Friday's lab. It is recommended that you have this homework mostly completed before you leave for Spring Break.
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. Friday's lab will be due on Wednesday, March 24.
4. When you return from Break on March 22, your instructor will still be out of town (working, not on vacation). As usual, a subsitute will take the class that day. Also, there will be no office hours that day.

Assignments

• Monday, Mar. 8, Sec. 4.5 / #1, 3, 8, 9, 11, 13, 19, 20, 21, 23, 25, 33, 34
• Wednesday, Mar. 10, Sec. 4.6 / #1, 2, 5, 7, 9, 13, 17, 18, 19, 24, 26
• Friday, Mar. 12, Sec. 4.9 / #(1), (2), 7, (9), 10, 11, 12

Last modified: February 11, 1999