MAT 342  Linear Algebra
FALL 2006*

  *Important Note:All items on this syllabus are subject to change.
Any in-class announcement, verbal or written, is considered
official addendum to this syllabus.
Course Description
Homework Problems
Related Web Sites
Important Info(HW,Labs&Tests)
Back to Suslov's home page


Course:           MAT 342, Linear Algebra
Time:              8:40 - 9:30 am, MWF
Location:         PSA 309
Line #:             60136
Instructor:       Dr. Sergei Suslov
Office:             PSA 621
Phone:             965-8987
Office Hours: 11:40 am– 12:30 pm MWF or by appointment
Text:                Linear Algebra with Applications, 7th edition,
                         by Steven Leon, 2006
Prerequisite:   MAT 272 or equivalent
Exams:            There will be three regular in class exams (3*100);
                         homework, quizes and/or computer labs (100);
                         and a comprehensive final exam (200)
Grading Policy:
                         A-, A, A+ = 90 - 100%
                         B-, B, B+ = 80 - 89%
                         C, C+ = 70 - 79%
                         D = 60 - 69%
                         E = 0 - 59%
Material to be covered: Except for a few sections, chapters 1-6 will be covered
Make-up policy: No make-up exams will be given without notification.
                            Also, no late homework will be accepted for grading.

Course Description

MAT 342 is a linear algebra course at the sophomore/junior level, intended primarily for mathematics,
science and engineering students. The goal of the course is to impart the concepts and techniques
of modern linear algebra (over the real scalar field) with a significant level of rigor.
The prerequisite is coregistration in MAT 272.

The successful student will be able to write clearly about the concepts of linear algebra,
(definitions, counterexamples, simple proofs),and to apply the theory to examples.
Some exposure to the practical nature of solutions of linear algebra problems is healthy.
On the other hands, sophisticated numerical algorithms should not be presented.

Use of computers to work numerous problems often can enhance the student’s understanding
of the material. It is suggested that a software package be made available to the students,
but that classroom discussion of computers be limited. Instructors are encouraged,
but not required, to make use of computers in the course.

Below is a list of recommended topics, together with approximate class times for each section.
If time permits, applications (e. g. least-squares, LU decomposition, difference equations,
dense vs. sparse matrices, etc.), or an introduction to complex vector spaces may be included.

# Systems of linear equations and matrices            (6  50-minute classes)
Gauss-Jordan elimination, homogeneous systems, matrix algebra, elementary matrices, inverses

# Determinants                                                     (3  50-minutes classes)
 by row reduction and cofactor expansions, Cramer’s rule

# Vector Spaces                                                   (9  50-minutes classes)
Euclidean space, general (real) vector spaces, subspaces, linear independence,
dimension, row, column and null spaces

# Inner products                                                    (5  50-minutes classes)
norms, orthogonal bases and Gram-Schmidt orthogonalization

# Linear transformations                                         (8  50-minutes classes)
Kernel and range, inverse transformations, matrices of linear transformations,
change of basis, similarity

# Eigenvalues and eigenvectors                               (7  50-minutes classes)
diagonalization, orthogonal diagonalization and symmetric matrices, quadratic forms

Suggested MAT 342 Homework Problems

Section                 Problems

1.1                         11/1a,1c,2,3,4,5a,5b,5c,6a,6c,6f,11
1.2                         25/1,3,4,5b,5d,5e,5h,6b,11,13,17
1.3                         57/1,2,3,4,8b,8d,12,14,15,16
1.4                         69/2,9,10c,10f,10g,11a,21         

2.1                         96/2,3c,3e,3g, 3h,5,6,11
2.2                         103/1(a)-(c),3(a)-(e),5,6,13
2.3                         109/1c,2a,2c

3.1                         121/1,4,6*,9
3.2                         131/1*,2*,3,4*,5,9a,b,11,14*,17,18,20
3.3                         144/2*,5,7*,11*,14,15,16,17
3.4                         150/ 3*,5*,9,10,11*
3.5                         161/1*,2*,5,7,8*
3.6                                             167/1*,2,4b,4d,4e,6,7,11,15*,20

4.1                         182/1*,3*,4,6*,7,8,9,11,12*,16,19*,22,24
4.2                         196/1*,2*,3*,4,5,13

5.1                         223/1a,1d*,7,12*  
5.4                         252/1*,2(a)*,3*, 7, 17,24*,29
5.6                         281/1b,3*,7,8*

6.1                         310/1(a)-(f)*,2(a)*,3,5*,6,8*,10,13*,17*,22
6.2                         323/1(a)-(c)*,2(a)-(c)*
6.3                         340/1b,1e,2b,2e,3b,3e,4a,6,8c,13,15

*homework problem to review

Related Web Sites:

Leon Linear Algebra Textbook Homepage
Linear Algebra WebNotes by Dr. Mark V. Sapir
Linear Algebra WebNotes by Dr. Beth Novick
Elementary Linear Algebra
(Lecture Notes by Keith Matthews, 1991)
Linear Algebra Website,
Department of Mathematics, Arizona State University
History of Mathematics Archive

I Hate Linear Algebra Home Page
Top Ten Suggestions on Teaching Linear Algebra

The Maple Computer Algebra System


HW#1, sections 1.1-1.2: due to Friday, September 1
HW#2, sections 1.3-1.4: 2.1-2.3 due to Monday, September 25.
HW#3, sections 3.1-3.6 due to Friday, October 20.
HW#4, sections 6.1-6.2 due to Friday, November 3
HW#5, sections 4.1-4.2, 5.1, 5.4, 5.6 due to Monday, December 4

Computer labs
Lab#1, "Introduction to Maple V":
Lab#2, "Gauss-Jordan elimination":
Lab#3, "Matrix Algebra":
Lab#4, "Matrix Inversion, Determinants, and Cramer's Rule":
Lab#5, "Vector Spaces, Independence, Basis, and Dimension":
Lab#6, "Row Space, Column Space, and Nullspace":
Lab#7, "Gram-Schmidt process, Eigenvalues and Eigenvectors":

Test#1, Monday, September 25
Test Review Friday, September 22
Sections 1.1-1.4 and  2.1-2.3 are on the test.
Problems to review:
1.1: # 6(d)-(f)
1.2: # 6(a)-(d)
1.3: # 1(a)-(h), 2(a)-(f), 5, 8
1.4: # 9(a)-(h)
2.1: # 2(a)-(c), 3(a)-(h), 4, 5
2.2: # 1(a)-(c), 3, 5, 6, 10
2.3: # 1(a)-(d), 2(a)-(e)
You may use your calculators if you wish during the test but I will not accept "calculator's" solutions!
You must show your work in order to get the full credit!

Test#2, Friday, November 3
Test Review Wednesday, November 1
Sections 3.1-3.6 and  6.1-6.2 are on the test.
Problems to review: see homework problems with * above

Test#3, Monday, December 4 or Tuesday, December 5 (in the testing center!!!)
Test Review Monday, December 4
Sections 4.1-4.2 and  5.1, 5.4, 5.6 are on the test.
Problems to review: see homework problems with * above

Quiz#1, Friday, October 20
Sections 3.1-3.6 are on the quiz.
Wednesday, November 15

Sections 3.1-3.6 and 6.1-6.2 are on the quiz.

Final Exam:  Tuesday, December 12, 7:40 - 9:30 am, PSA 309
Reviews:  Monday, December 4 (regular time and place), Wednesday, December 6 (PSA 304, 10-11:15 am)