21-341: Linear Algebra

Scheduling Information

Exam Time:
8:30-11:30 in MM 103.

Review Sessions: Tentatively scheduled for

Wednesday 7 May, 11:30-12:30, WEH 8427. (Definition 24.6, Corollary 24.7 and Theorem 24.8)
Sunday 11 May, 3:00-4:30, WEH 8427. (general review)

Office Hours: For exam week

11:30-12:30 and 4:00-5:00 Friday (May 9)
11:30-12:30 Monday (May 12)


Your graded HW#14 is available in my office.
Solutions to selected homework assignments are available to the right of my office door.

Exam Solutions:

Your graded Exam #3 can be picked up from my office.
Solutions to Exam #1 are available to the right of my office door.
Solutions to Exam #2 are available to the right of my office door.
Solutions to Exam #3 are available to the right of my office door.

Exam #3 Review:

Reading: The Final Exam is comprehensive, covering

Chapter 1. Introduction to Linear Algebra
Chapter 2. Vector Spaces and systems of Linear Equations
Chapter 3. Linear Transformations and Matrices
Chapter 4. Vector Spaces with an Inner Product
Less emphasis on Section 14.
Chapter 5. Determinants
Chapter 6. Polynomials and Complex Numbers
Some results from Section 20 (e.g. division process)
Chapter 7. The Theory of a single Linear Transformation
Sections 22, 23, 24.
You should be able to prove Corollary 24.7 and Theorem 24.8, as well as the proposition that precedes them.
Section 25 omitted.

What to expect:
Approximately 1/3 of the exam will be calculations and examples, the remainder will be more theoretical exercises.

You should review the main theorems and techniques from each section. You will not be required to memorize proofs, but you should have a general idea of what is involved. Similarly with homework problems.

When studying, try to avoid a "memorizing list of facts" mentality. Instead focus on "filling in pieces of a puzzle." A useful exercise might be to figure out for each theorem what previous theorems are used in the proof. This will show the relationships among the various ideas. It is easier to remember the ideas if they fit into some framework.

You might also try filling one side of a sheet of paper with all the most important ideas. Finished? Good. Now start over with a half sheet of paper. When you have finished with that, try again with a quarter sheet. Keep going...

Mathematics is a subject that is best learned by doing. You might do well to try solving some extra problems...

Exercises: I've already pointed out most of the good problems from the other sections, but here are some from Section 24.

Section 7.24 #3, 6, 7, 10ab (don't worry about expressing D and U as polynomials).