Math 544 Section 001 (TTh 12:30--1:45 PM), LeConte 405
Linear Algebra

Spring 2013

Professor: Peter J. Nyikos

Office: LeConte 406

Phone: 7-5134

Email: nyikos @ math.sc.edu

Prerequisite: MATH 241

Office hours Monday April 29: 2:00 - 4:00 [revised from earlier].
Tuesday April 30: 2:00-3:00 and 4:30 - 5:30
Wednesday May 1: 2:00-4:00
Thursday, May 2: 1:15-2:30
Friday, May 3: 9:00-12:30
Monday, May 6: 1:30 -4:00 pm

Homework, extra credit papers and test papers that have not yet been picked up are ready to be picked up.
Answer keys to the three tests, and the last homework, are available in envelopes outside the door of my office.

The final exam is on Tuesday, May 7, 12:30 - 3:00. It is cumulative, but special emphasis is given to Chapter 4, with problems similar to those on the homework and practice problems.

The first test in this course was on Tuesday, February 26, on Chapter 1 except for sections 1.4 and 1.8; also, Section 1.1 is just for familiarization of terminology.

The second test in this course was on Thursday, March 28, on Section 2.4 and on Sections 3.3, 3.4, and 3.5. Section 3.2 is just for familiarization of terminology.

The third test in this course was on Thursday, April 18, mostly on Section 3.6 and on Sections 3.7, but also on 2x2 and 3x3 determinants, and a number of proofs of theorems.

Textbook: Linear Algebra, by Johnson, Riess, and Arnold 5th ed.

The following sections will be covered to some extent, some thoroughly: 1.1 through 1.7; 1.9
2.3, 2.4
3.2 through 3.7
4.1 through 4.7
5.9

The final exam for this course is on May 7, starting at 12:30 pm.

Approximately once a week, except the first, there will be either a homework to turn in, or a quiz, or a test. There was a quiz on Tuesday, January 29 on Section 1.3.

There was a quiz on Tuesday, February 5, on Section 1.5.
There was a quiz on Tuesday, February 12, on Section 1.7.
There will be a quiz on Tuesday, April 16 on Section 3.7, finding the matrix A such that T(x) = Ax for all vectors in the domain of T.

Further information on grading and policies can be found here in pdf format.

Learning Outcomes: Students will master concepts and solve problems based upon the topics covered in the course, including the following: solutions of systems of linear equations; Gaussian elimination; matrix multiplication and calculation of inverses; linear transformations and their associated matrices and their geometric interpretations; parametrized solutions to systems of linear equations; vector spaces and subspaces including null spaces and column spaces of matrices; rank and nullity of matrices; bases for, and dimensions of subspaces; determinants, eigenvalues, eigenvectors and the characteristic equation; inner products; orthogonal and orthonormal sets, and the Gram-Schmidt process for producing them; and least squares solutions to data problems.

Practice Problems
Section 1.1: problems 11, 13, 21, 23, 27, and 33.
Section 1.2: problems 3, 5, 9, 23, 29, 45.
Section 1.3: problems 3, 19, 21, 23
Section 1.5: numbers 1, 3, 11, 13, 21, 23, 31, 33, 43
Section 1.6: numbers 1, 3, 7, 9, 13, 19, 21, 29, 41
Section 1.7: numbers 3, 5, 9, 13, 17, 23, 29, 37, 39
Section 1.9: numbers 1, 9, 15, 17, 29, 39
Section 3.2: problems 1, 3, 9, 11
Section 3.3: problems 23, 25, 27, 31
Section 3.4: problems 5, 7, 9, 11, 13, 15
Section 3.5: problems 1, 3, 9, 13, 21, 23, 25
Section 3.6: problems 1, 5, 9, 13, 19
Section 3.7: problems 1, 3, 13, 15, 21, 23, 25
Section 4.1: problems 3, 5, 7, 13
Section 4.2: problems 9, 13, 15,17
Section 4.3: problems 1, 7, 19

Homework to be handed in:
Handed in Thursday, January 24:
1.1, numbers 18,20, 22
1.2, numbers 10, 20, 24, 28, 32, 50, 54

Hand in Thursday, February 14:
1.3, number 4
1.5, numbers 6, 26, 44
1.6, numbers 10, 22
1.9, numbers 18, 30, 38

Hand in Tuesday, April 2:
3.3, numbers 32 and 48 (technique optional)
3.4, number 36
3.5, numbers 12, 14, 20

Extra Credit

Extra credit problems are assigned from time to time. They are to be done strictly on your own, except that I am willing to give you advice. You are not to discuss them with anyone else.

There is no due date for extra credit, but once a fully correct solution is handed back, the problem is no longer eligible for extra credit. This is true of all problems with lines through them below.
If you can't quite get the solution to an extra credit problem but have some ideas, hand it in for partial credit. I will keep adding to your score as you improve your work on it.

1. Problem 2, page 44 [worth 8 points; be sure to justify answer to (c)] [ineligible as of start of class on Tuesday, April 2]

2. Section 3.8, Problem 2

3. Section 3.8, Problem 8

4. Section 3.9, Problem 2

5. Section 4.5, Problem 12

6. Section 4.7, Problem 8 (note Theorem 19, page 327)

7. Section 4.8, Problem 8 (omit calculation of x subscript 10) 8. Section 4.8, Problem 10 (omit calculation of x subscript 10)