MATH 228 Linear Algebra
Text: Linear Algebra by Jim Hefferon
The text is free. You may download the text and solutions to exercises at:
http://joshua.smcvt.edu/linearalgebra
Instructor: Yuanqian Chen
Office: Marcus White 112
Phone: 832-2858 (office) 676-9511 (home)
E-mail: chen@ccsu.edu
Office Hours: Mondays & Wednesdays: 9:45-10:45am; 12:35-3:00pm;
Tuesday 2:20-3:20pm
or by appointment. Please feel free to stop in anytime, an appointment is not necessary.
Students for Whom Course Is Intended:
B.S. math majors (required)
B.A. math majors (required)
B.S. and B.A. concentrates (elective)
Basic Goals of Course:
1. To introduce matrices, determinants and vectors
2. To study systems of linear equations by means of matrices and determinants
3. To introduce the concept of finite dimensional vector space
4. To relate and apply matrices to linear transformations
Topics covered:
Chapter 1
Linear Systems
I. Solving Linear Systems
I.1
Gauss’s Method
I.2
Describe the Solution Set
I.3
General=Particular + Homogeneous
II. Linear Geometry
II.1
Vector in Space
III. Reduced Echelon Form
III.1 Gauss-Jordan Reduction
III.2 The Linear Combination Lemma
Chapter 2
Vector Spaces
I. Definition of Vector Space
I.1
Definition and Examples
I.2
Subspaces and Spanning Sets
II. Linear Independence
II.1
Definition and Examples
III. Basis and Dimension
III.1 Basis
III.2 Dimension
III.3 Vector Spaces and Linear Systems
Chapter 3
Maps Between Spaces
I. Isomorphism
I.1 Definition and Examples
I.2 Dimension Characterizes Isomorphism
II. Homomorphism
II.1
Definition
II.2
Range Space and Null Space
III. Computing Linear Maps
III.1 Representing Linear Maps with Matrices
III.2 Any Matrix Represents a Linear Map
IV. Matrix Operations
IV.1 Sums and Scalar Products
IV.2 Matrix Multiplication
IV.3 Mechanics of Matrix Multiplicaiton
IV.4 Inverses
V. Change of Basis
V.1
Changing Representations of Vectors
V.2
Changing Map Representations
Chapter 4
Determinants
I. Definition
I.1
Exploration
I.2
Properties of Determinants
I.3
The Permutation Expansion
II. Geometry of Determinants
II.1
Determinants as Size Function
Topics: Cramer’s Rule
Chapter 5
Similarity
Complex Vector Spaces
I.1
Polynomial Factoring and Complex Numbers
I.2
Complex Representations
II. Similarity
II.1
Definition and Examples
II.2
Diagonalizability
II.3
Eigenvalues and Eigenvectors
Grading:
Three Tests (100 minutes, 100 points each)
300
Final Exam (120 minutes, 150 points)
150
------450
If your total points are: 405--450, you will get at least A-.
360--404, you will get at least B-.
315--359, you will get at least C-.
270--314, you will get at least D-.
This is exactly how your grade will be calculated:
405-419: A360-374: B315-329: C270-284: D-
420-450: A
375-389: B
330-344: C
285-299: D
390-404: B+
345-359: C+
300-314: D+
Test Date:
First Test: Wednesday, February 17,
Second Test: Wednesday, March 16,
Third Test: Wednesday, April 20.
Final Exam: Wednesday, May 11, 8:00am-10:00am
Withdrawal Policy:
Monday, February 8: Last day to drop full semester course without "W"
Monday, April 18: Last day to withdraw from the courses without approval. "W" will be entered;
After April 18, students need permission of instructor and department chairperson to withdraw
from a course.
In the event of a weather emergency with required curtailment or cancellation of classes, listen to
WTIC (1080AM) or call (860)832-3333 for the General Snow Messages.
If you need course adaptations or accommodations because of a disability, if you have
emergency medical information to share with me, or if you need special arrangements in case the
building must be evacuated, please make an appointment with me as soon as possible.
Assignment of Linear Algebra
Chapter/Section
Chapter 1
I.1
I.2
Page
Exercises
9
19
I.3
II.1
III.1
III.2
32
41
54
62
1.17, 1.18, 1.20, 1.22, 1.25, 1.29
2.15, 2.16, 2.17, 2.18(d),(e), 2.19(b),(c), 2.31, 2.24, 2.28,
2.29
3.15, 3.17, 3.20, 3.21, 3.24
1.1, 1.3, 1.4, 1.7
1.8(d), 1.10, 1.13, 1.14, 1.15
2.10, 2.17, 2.19
Chapter 2
I.1
I.2
II.1
III.1
III.2
III.3
86
97
109
117
124
132
1.18, 1.19, 1.21, 1.22, 1.24, 1.28, 1.29, 1.32
2.20, 2.21, 2.22, 2.23, 2.25(a), (d), 2.26, 2.27, 2.29,2.36
1.20, 1.21, 1.22, 1.28, 1.31, 1.32,1.35
1.18, 1.19, 1.20, 1.21, 1.23, 1.29, 1.32, 1.33
2.16, 2.17, 2.18, 2.22, 2.26
3.17, 3.18, 3.26, 3.21, 3.23(a)(b)(c), 3.24, 3.26, 3.29, 3.32
Chapter 3
I.1
I.2
II.1
III.1
IV.1
IV.2
IV.4
170
179
186
209
228
230
249
1.13, 1.15, 1.16, 1.17, 1.18, 1.23, 1.24, 1.25, 1.35, 1.37
2.9, 2.10, 2.11, 2.12, 2.16, 2.23
1.18, 1.20, 1.22, 1.25, 1.27, 1.29, 1.31
1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.24
1.8, 1.15, 1.16
2.14, 2.15, 2.16, 2.17, 2.18
4.13, 4.14, 4.15, 4.15, 4.29