Math 429 Fall 2010

Math 429: Linear Algebra

FALL 2010

Time Location Instructor email Office
M-W-F 12:00-1:00 PM Lab Sciences, Room 201
Roya Beheshti
beheshti@math.wustl.edu Cupples I, Room 107A



Welcome to the webpage for Math 429. This course is an introduction to linear algebra of finite-dimensional vector spaces.
Topics include: systems of equations, matrices, determinants, inner product spaces, and spectral theory.

Prerequisites: Math 310 or permission of instructor

Textbook: Linear Algebra by K. Hoffman and R. Kunze
Here are two other books that may be useful:
1) Nering, Linear Algebra and Matrix Theory (this book is on a 2-day reserve at Olin library),
2) Jim Hefferon, Linear Algebra . This book is free to download (scroll down to where it says "Here is Linear Algebra").

Office hour: Tuesday 2:30-4:30pm, Wednesday 2:00-3:00pm, and by appointment

Homework: There will be weekly homework. The homework is due on Wednesdays (starting from Wednesday September 15) at the beginning of class. Late homework will not be accepted.
You are encouraged to discuss the problems but the write-up must be your own. The grader for this course is Bingyuan Liu (bingyuan@math.wustl.edu).
I expect there will be 12 problem sets. The two lowest homework grades will be dropped and the remaining 10 will be counted towards your final course grade.

Exams: There will be two in class midterm exams during the semester. The first midterm is scheduled for Friday October 8th, and the second midterm is schedule for Monday November 15.
There will also be a final exam. If you are unable to take one of the midterm exams for legitimate reasons, you will not be given a make up exam.

The list of the theorems you need to know for the first midterm exam can be found here .
The list of the theorems you need to know for the second midterm exam can be found here .
Solutions to the second midterm exam .
The list of the theorems you need to know for the final exam can be found here .

Grading Information: The midterms and the homework will each count for 20 percent of your grade. The final exam will count for 40 percent of your grade.
Your letter grade will be based on the scale appearing in the following table.

Numerical Grade Letter Grade
[90,100] A
[80,90] B
[65-80] C
[50-65] D
[0,49] F



Homework assignment :
1. (Due 9/15) Page 5: 7; Page 10: 2, 5; Page 15: 2; Page 21: 4; Page 27: 10
2. (Due 9/22) Page 34: 4, 7; Page 39: 4, 7, Page 48: 4, 10, 12
3. (Due 9/29) page 48: 7; Page 55: 2, 3, 7; Page 66: 3, 6
4. (Due 10/6) Page 73: 5, 7, 9 ; Page 83: 3, 5 (you should describe T^2)
5. (Due 10/20) Page 86: 3; Page 95: 5, 7, 12; Page 105: 2, 3, 11
6. (Due 10/27) Page 106: 12, 13; Page 115: 1; Page 148: 1(a,b,d,f), 6; Page 155: 4
7. (Due 11/3) Page 107: 17 (Do this problem for n=2 first to see the pattern) ; Page 162: 1, 3, 7, 9
Solutions to the selected problems from Hw#5--7 can be found here .
8. (Due 11/15) Page 163: 2 (a), 8; Page 189: 4, 6, 7, 10
9. (Due 11/22) Page 190: 8, 9, 13; Page 198: 3; Page 205: 1; Verify the Cayley-Hamilton Theorem for diagonalizable matrices.
Solutions to the selected problems from Hw#8,9 can be found here .
10. (Due 12/1) Page 198: 7 (choose a basis, represent D with respect to that basis, and find the characteristic polynomial of D); Page 205: 3, 4, 5 (you can use any theorem stated in class); Page 213: 2; Page 225: 1
Solutions to the selected problems from Hw#10
11. (Due 12/8) Page 250: 5; Page 275: 2, 5, 8; Page 289: 5, 9.
Solutions to the selected problems from Hw#11
12. Page 289: 4, 6, 12, 13
Solutions to the selected problems from Hw#12