Course:
MAT 342, Linear Algebra
Time:
10:40 - 11:30, MWF
Location:
PSH 552
Line #:
88308
Instructor:
Dr. Sergei Suslov
Office:
PSA 643
Phone:
965-8987
E-mail:
sks@asu.edu
Office Hours: 9:30 – 10:25
am and 1:45 – 2:30 pm MWF
Text:
Linear
Algebra with Applications, 5th edition,
by Steven
Leon, 1998
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 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
p. 11, #: 1a, 1c*, 2, 3*, 4, 5a, 5b*, 5c*, 6a, 6c, 6f*, 7, 11*
1.2
p. 25, # 1*, 3*, 4, 5b, 5d*, 5e, 5h, 6b*, 11*, 13, 16
1.3
p. 53, # 1*, 2*, 3, 4*, 8b, 8d*, 12*, 14, 15*, 16, 17*, 22, 31
1.4
p. 65, # 1, 2, 3a, 4c, 7a, 7d, 8*, 9c*,11a, 15a, 21
1.5
p. 74, # 1, 3, 4*, 7, 9*, 11, 13, 14, 15
2.1
p. 90, # 2*, 3c*, 3e*, 3g*, 5*, 10, 11, 12
2.2
p. 97, # 1c*, 2, 3e*, 5*, 6*, 10*, 11*,13, 16
2.3
p. 103, # 1a-d*, 2a-d*
3.1
p. 114, # 1, 4*, 6*, 9*, 11*, 15, 16
3.2
p. 123, # 2*, 3, 4*, 5, 9, 11*, 14, 17, 18, 19, 20*
3.3
p. 135, # 2*, 3, 5*, 7*, 11*, 14, 15, 16, 17*
3.4
p. 141, # 2, 5*, 8*, 9*, 10, 13*, 17
3.5
p. 152, # 1*, 2, 5*, 7, 8, 11
3.6
p. 159, # 1*, 2, 3, 4b*, 4d*, 4e, 4f, 5, 6, 7, 8, 9, 10*, 11, 12, 15,
19
4.1
p. 172, # 1*, 3*, 4, 6*, 7, 8*, 9, 11, 12*, 16*, 19, 20, 21,
22, 24
4.2
p. 184, # 2*, 3(a)-(b)*, 4*
4.3
p. 192, # 1*, 2*, 6, 13*
5.1
p. 206, # 1a*,1d*, 2a, 2d, 3c, 3d, 5*, 7b, 8, 10*, 11
5.2
p. 215, # 1, 2, 3, 4, 5*, 9, 11, 12, 13, 16 (optional)
5.3
p. 224, # 1*, 2*, 8*, 12*, 13, 14, 16, 17*, 24*
5.5
p. 253, # 1*, 2*, 4*, 6*, 7*, 8*
5.6
p. 265, # 3*, 4*, 8*
6.1
p. 289, # 1a*, 1c*, 1f*, 1h*, 2*, 5, 11*, 13, 18*, 19
6.2
p. 302, # 1a*, 1e*, 2a*, 2b*
6.3
p. 316, # 1a* - f*, 2b*, 2e*, 3a*, 3e*, 4a, 6*, 8c
6.4
p. 327, # 1b*, 2*,
3, 4, 5a*, 5d*, 7, 9*.
6.5
p. 342, # 1, 3b, 4, 5, 6a, 6b, 6c, 7e, 7f, 10 (optional)
6.6
p. 350, # 1, 3, 4a, 4c, 5a, 5c, 8, 13 (optional)
*homework problem for grading
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
Homework
HW#1, sections 1.1-1.2: due
to Monday, Feb 1.
HW#2, sections 1.3-1.5: due
to Monday, Feb 15.
HW#3, sections 2.1-2.3: due
to Wednesday, Feb 24.
HW#4, sections 3.1-3.3: due
to Friday, March 12.
HW#5, sections 3.4-3.6, 4.1-4.3:
due to Monday, April 5.
HW#6, sections 5.1-5.3, 5.5,
5.6: due to Wednesday, April 21.
HW#7, sections 6.1
- 6.6: due to Monday, May 3
Computer labs
Lab#1,
"Introduction to Maple V": Wednesday, Jan. 27,
room ECA 221, 10:40-11:30 am.
Lab#2,
"Gauss-Jordan elimination": Wednesday,
Feb. 3,
room ECA 221, 10:40-11:30 am.
Lab#3,
"Matrix Algebra": Wednesday,
Feb. 10,
room ECA 221, 10:40-11:30 am.
Lab#4,
"Matrix Inversion, Determinants, and Cramer's Rule":
Wednesday, Feb. 17,
room ECA 221, 10:40-11:30 am
Lab#5,
"Vector Spaces, Independence, Basis, and Dimension":
Wednesday, March 10,
room ECA 221, 10:40-11:30 am
Lab#6,
"Row Space, Column Space, and Nullspace":
Wednesday, March 31,
room ECA 221, 10:40-11:30 am
Lab#7,
"Gram-Schmidt process, Eigenvalues and Eigenvectors":
Monday, April 26,
room ECA 221, 10:40-11:30 am
Tests
Test#1,
Wednesday, Feb. 24
Test Review,
Monday, Feb 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,
Monday, April 5
Test Review, Friday, April 2
Sections 3.1-3.4, 3.6 and
4.1-4.3 are on the test.
Problems to review:
3.1: # 4-6, 16
3.2: # 2, 3, 4(a), (c), 6, 11, 20
3.3: # 2, 5, 7, 11, 15
3.4: # 2, 4, 5, 8, 14
3.6: # 1, 4(a), (d), 10.
4.1: # 1, 3, 6, 8, 12, 16
4.2: # 2, 3, 4
4.3: # 1, 2, 13
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#3,
Monday, May 3
Test Review, Friday, April 30
Sections 5.1, 5.3, 5.5, 5.6
and 6.1-6.4 are on the test.
Problems to review:
5.1: # 1a,1d, 2a, 2d, 7b,10
5.3: # 1, 2, 7, 8, 12, 17, 24
5.5: # 1, 2, 4, 6, 7, 8
5.6: # 3, 4, 8
6.1 # 1a, 1c, 1f, 1h, 2, 5, 13, 18, 19
6.2 # 1a, 1e, 2a, 2b
6.3 # 1a - d, 2b, 3a, 4a
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!
Final
Exam: Monday, May
10, 12:20-2:10 pm, PSH 552
Reviews:
Wednesday, May 5, PSH 552, 10:40-11:30
am
Thursday, May 6, PSA 306, 9:00-10:15
am
HAVE A NICE SUMMER!