# Math 544 Section 001 (MTWTh 1:00--3:15, with a 15 minute break), LeConte 405 Linear Algebra

Summer I

Professor: Peter J. Nyikos

Office: LeConte 406

Phone: 7-5134

Email: nyikos @ math.sc.edu

Prerequisite: MATH 241

Office Hours:
MTWTh 10:30 - 12:15
Other times by appointment (or you could try dropping by if you are close by anyway); exceptions announced in advance when possible and posted on office door.

Three times a week, there will be either a homework to turn in, or a quiz, or an hour test.

Textbook: Linear Algebra, by David C. Lay, 4rd ed. ISBN: 9780321385178

The course covers parts of the following sections:

• 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.9;
• 2.1, 2.2, 2.3, 2.8, 2.9:
• 3.1, 3.2, 3.3;
• 4.1, 4.2, 4.3, 4.5, 4.6;
• 5.1, 5.2, 5.3;
• 6.1, 6.2, 6.3, 6.4, 6.5.

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.

I last taught this course in 2005, but from a different textbook. If you are interested in details, go here.

First week Monday (Memorial Day!) we covered Sections 1.1 and 1.2; Tuesday we covered 1.3. and much of 1.4, and had a quiz on 1.2; Wednesday we finished 1.4, covered 1.5, and had a quiz on 1.3. Thursday we covered 2.1 and 2.2 not dependent on Section 1.8 (which is to be covered the second week).

Homework handed in on Thursday, June 2:
Section 1.1. Exercises 12, 14.
Section 1.2. Exercises 4, 14.
Section 1.3. Exercise 12.
Section 1.4. Exercise 12.

Second week
Monday, June 6: we covered most of Section 1.7 and had a quiz on 1.5. Tuesday there was a quiz on 2.1 and 2.2.

Homework handed in on Thursday, June 9:
Section 1.5. Exercises 12, 18 (omit geometric comparison).
Section 1.7. Exercises 6, 12.
Section 1.8. Exercises 10, 12.
Section 2.1. Exercise 2.
Section 2.2. Exercise 31 (Show your work!).

Third week
The Midterm was on Monday, June 13. It covered all sections covered on the homework of the first two weeks, except 1.8. There was a quiz Tuesday on Sections 1.8 and 1.9.

Homework handed in on Thursday, June 16:
Section 1.9. Exercises 8, 10.
Section 2.1. Exercise 12.
Section 2.2. Exercise 2.
Section 2.8. Exercises 12, 24.
Section 2.9. Exercise 12.

Third week
There is a quiz Monday, June 20 on Sections 3.1 and 3.2.

Homework handed in on Thursday, June 23:
Section 3.1. Exercise 14.
Section 3.2. Exercises 24, 26.
Section 3.3. Exercise 24.
Section 4.1. Exercise 28.
Section 5.2. Exercise 14.
Section 5.3. Exercise 14.

Homework handed in Monday, June 27:
Section 6.1. Exercises 2, 10.
Section 6.2. Exercises 2, 6.
Section 6.3. Exercises 12, 16.

Here are some exercises to study; you are strongly advised to work some of them even though they are not to be handed in.

Section 1.1. Practice Problems, and Exercises 11, 13, 31.
Section 1.2. Practice Problems, and Exercises 1 and 3.
Section 1.3. Practice Problem 2, and Exercises 11 and 23.
Section 1.4. Practice Problems, and Exercises 5, 7, 11 and 23.
Section 1.5. Practice Problems, and Exercises 1, 7, 11 and 13.
Section 2.1. Practice Problem 2, and Exercises 1, 3, 7, and 27.
Section 2.2. Practice Problems, and Exercises 1, 3, and 7b.

Section 1.7. Practice Problems, and Exercises 1, 3, 5, 9, and 11.
Section 1.8. Practice Problems, and Exercises 1, 3, 11, 17, and 19.
Section 1.9. Practice Problems, and Exercises 3, 5, 11, and 15.

Section 2.3. Practice Problems, and Exercises 1, and 7.
Section 2.8. Practice Problems, and Exercises 1, 7, 11, 23 and 25.
Section 2.9. Practice Problems, and Exercises 3 and 9.
Section 3.1. Practice Problem, and Exercises 1, 9, 11, 13, and 19.
Section 3.2. Practice Problems, and Exercises 1, 3, 5, 7, 21 and 25.
Section 3.3. Practice Problem, and Exercises 19, 23, and 27.
Section 4.1. Practice Problem 1, and Exercises 1, 9, and 11.
Section 6.1. Practice Problems, and Exercises 1, 7, 13, 15 and 17.
Section 6.2. Practice Problems, and Exercises 3 and 5.
Section 6.3. Practice Problem, and Exercises 1, 7 and 11.
Section 6.4. Practice Problem, and Exercises 3, 7, and 9.
Section 6.5. Practice Problems, and Exercise 5.

### Extra Credit

Extra credit problems will be 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 includes problems with lines drawn through them.
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. Is there a 2x3 matrix A and a 3x2 matrix B such that AB = I_2 and BA = I_3? Here I_n stands for the nxn identity matrix. [Worth 10 points, as stated; 5 points with the knowledge that the answer is negative.]

2. Is there a 2x3 matrix A and a 3x2 matrix B such that AB = I_2?

3. Section 1.9, Exercise 26

4. and 5. Section 2.4, Exercises 8 and 22.

6. Show that similarity of matrices is transitive: if A is similar to B and B is similar to C, show that A is similar to C.

7. Exercise 6, page 261

8., 9. and 10. Section 5.6, Exercises 2, 6 and 12.