21-341: Linear Algebra

Scheduling Information

Exam Time:

11:30-12:20 (regular class time) in DH 2122 (regular class room).

Review Session:

Monday 28 April, 7:30-9:00pm, in DH 2105.

Homework: Your graded HW#13 will be returned in class on Monday.

Exam #3 Review:

Reading: The exam covers the following sections

4.14. The Concept of Symmety

4.15. Inner Products

5.16. Definition of Determinants

5.17. Existence and Uniqueness of Determinants

5.18. THe Multiplication Theorem for Determinants

5.19. Further Properties of Determinants

7.22. Basic Concepts (in the Theory of a single Linear Transformation)

7.23. Invariant Subspaces

What to expect:
Approximately 1/3 of the exam will be calculations and examples, the rematinder 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: You should not rely exclusively on these problems for your studying, but they can be a big help.

Section 4.14 #1, 4.

Section 4.15 #4, 6, 7, 10.

Section 5.16 #4.

Section 5.17 #1.

Section 5.18 #3, 4.

Section 5.19 #5, 9, 10.

Section 7.22 #1, 2, 6, 7.

Section 7.23 #6, 7, 8.