**Instructor:**
Dr. Sergei Suslov
**Office: **
PSA 643
**Phone: **
965-8987
**E-mail: **
*suslov@math.la.asu.edu*
**Office Hours:** 9:40 – 10:15
am and 1:15 – 2:00 pm MWF
**Text: **
*A First Course in Linear Algebra*, 2nd edition,

by Moore & Yaqub, 1996
**Prerequisite:** MAT 272
or equivalent
**Exams: **
There will be three regular in class exams (3*100);

homework and/computer labs (100);

and a comprehensive final exam (200)
**Grading Policy:**

A = 90 - 100%

B = 80 - 89%

C = 70 - 79%

D = 60 - 69%

E = 0 - 59%
**Material to be covered: **Except
for a few sections, the entire text will be covered
**Make-up policy:** No make-up
exams will be given without notification.

Also, no late homework will be accepted for grading.

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 **required 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**
1, 6, 13, 14, 16, 20, 31, 41, 42, 53, 54, 55
**1.2 **
7, 8, 9, 10, 11, 12, 17, 20, 32, 33, 34
**1.3**
1*, 3, 7, 9*, 10, 11, 12, 13, 22*
**1.4
**1, 2, 3, 4, 5, 6, 9*, 10, 16*, 21, 22, 23*
**1.5
**1, 2, 3, 4*, 5, 7, 15*, 20, 25, 29*, 31, 39

**2.1**
1, 2, 3, 8*, 9, 17, 18, 21, 24, 25, 27*, 29*, 30, 41
**2.2
**1, 2, 3*, 4*, 5, 6, 15*, 17, 18, 19, 44
**2.3**
1*, 2*, 4, 8*, 10, 11*, 14*, 15, 18, 36, 37
**2.4**
2, 3, 4, 5*, 12*, 13, 14*

**3.1**
6, 10, 12*, 16, 18*, 29, 31*, 34, 37, 38, 39*, 40
**3.2**
12*, 25, 26, 28*, 29*, 35, 39*, 42, 43
**3.3 **
2, 5*, 8, 10, 11*, 12, 13, 14*, 15, 21, 23*, 24, 46
**3.4
**1*, 2, 3, 4*, 13, 14*, 16, 17, 21*, 26

**4.1
**11, 15, 28*
**4.2**
1, 10*, 42, 43
**4.3 **
7*, 12, 14*, 24, 25*, 26, 31, 34*, 42*, 51*, 53
**4.4**
8, 16, 24*, 28, 29*, 38, 40 (should read p(x)=x2), 44
**4.5**
1*, 5, 9*, 14, 16, 20*, 26
**4.6
**1, 6*, 9, 11*, 26

**5.1**
1 – 8*, 10, 16, 31*, 32, 42
**5.2**
1 – 6*, 20*, 25, 28*, 29
**5.3**
9*, 11, 12*, 29, 33*, 35
**5.4
**1 – 16*, 24, 25, 43
**5.5**
1 – 5*, 9, 37*
**5.6
**1 – 6*, 10, 12*, 22

**6.1**
1*, 7*, 28*, 29*, 30*, 31, 43*
**6.2**
1, 6, 7, 10, 12, 14, 29
**6.3**
2*, 9*, 11*, 16, 23*, 27
**6.4
**19, 25, 57 – 59
**6.6**
1, 3, 7, 8, 33

*homework problem for grading

Linear
Algebra WebNotes by Dr. Mark V. Sapir

Linear
Algebra WebNotes by Dr. Beth Novick

Elementary
Linear Algebra

(Lecture
Notes by Keith Matthews, 1991)

I
Hate Linear Algebra Home Page

Top
Ten Suggestions on Teaching Linear Algebra

Linear
Algebra Website,

Department
of Mathematics, Arizona State University

The
Maple Computer Algebra System

__Homework__
**HW#1**, sections 1.1-1.2: due
to ** Monday, Feb 2**.

__Computer labs__
**Lab#1**,
*"Introduction to Maple V"*: ** Wednesday, Jan. 28**,

room ECA 221, 8:40-9:30 am.

room ECA 221, 8:40-9:30 am.

room ECA 221, 8:40-9:30 am.

__Tests__
__Test#1__,
*Wednesday, Feb. 25;**Test Review*, *Monday,
Feb 23.*

Sections 1.1-1.5 and 2.1-2.4
of Chs 1&2 are on the test.

This test does not require a calculator,
but you may use one if you wish.

Homework, sections 2.1-2.4,
will be collected right after the test.
*Problems
to review*:

Chapter I, Review Exercises on p.
97: #1, 3, 7, 9, 10;

Chapter 2, Review Exercises on p.
141: #1, 2, 3, 5, 10;

and your homework problems!
__Test#2__,
*Monday, April 6**; Test Review, Friday, April 3.*

Sections 3.1-3.5 and 4.1-4.6 of Chs 3&4 are on test.

This test does not require a calculator, but you may use one if you wish.

Homework, sections 3.4 - 3.5, 4.1 - 4.6, will be collected right after the test.

Chapter 3, Review Exercises on p. 206: #1, 2, 3, 5, 7, 9, 11, 12, 14

Chapter 4, Review Exercises on p. 289: #1, 2, 3, 5, 7, 8, 10,

and your homework problems!

Sections 5.1-5.6 and 6.1, 6.3 of Chs 5&6 are on test.

This test does not require a calculator, but you may use one if you wish.

Homework, sections 5.4 - 5.6, 6.1, 6.3, will be collected right after the test.

Problems to review:

Chapter 5, Review Exercises on p. 366: #1-10

Chapter 6, Review Exercises on p. 455: #1-4, 7,

and your homework problems!

*HAVE A NICE SUMMER!!!*