MATH 3A

Course Content: Vectors, matrices, linear transformations, dot products, determinants, systems of linear equations, vector spaces, subspaces, dimension.

Textbooks: "Linear Algebra and its applications", 5th edition, by David Lay, Steven Lay and Judi McDonald.

Location: Lectures will be online: in SST 220B, MWF 12:00 p.m. - 12:50 a.m..
Discussion section: Joe Li, TBA.

My office hours: TBA.

Discussion section office hours: TAB.

Exams: There will be one midterm exams and a comprehensive final exam as stated below in the Course Schedule. No books are allowed on exams. The dates and times of all exams are fixed so make make sure that you have no conflicting plans. No make up exams and quizzes will be given under any circumstances. Please remember to bring your student ID to all exams.

Quizzes and homework: The homework assignments their due times are provided below. TA will conduct quizzes and collect homework at his/her discretion for grading. Diligent work on homework assignments is expected for its importance for the learning process.

Grading: The course grade will be based on quiz-homework, midterm and final exams in the following way: quizzes = 10%, homework grade = 10%, midterm exam = 35% and final exam = 45%.

Curve: The course grade may be curved if the median appears to be far below the B-/C+ region.

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Course Schedule and Homework

Lecture

Date

Section

Topic

4/01 M

1.1

Systems of Linear Equations

4/03 W

1.2

Row Reduction and Echelon Forms

4/05 F

1.3

Vector Equations

4/08 M

1.4

The Matrix Equation Ax=b

4/10 W

1.5

Solution Sets of Linear Systems

4/12 F

1.7

Linear Independence

4/15 M

1.8

Introduction to Linear Transformations

4/17 W

1.9

The Matrix of a Linear Transformation

4/19 F

2.1

Matrix Operations

4/22 M

2.2

The Inverse of a Matrix

4/24 W

2.3

Characterizations of Invertible Matrices

4/26 F

2.8

Subspaces of R^n

4/29 M

2.8, 2.9

Continued

5/01 W

2.9

Dimension and Rank

5/03 F

3.1

Introduction to Determinants

5/06 M

3.2

Properties of Determinants

5/08 W

3.3

Cramer's Rule, Volume and Linear
Transformations

5/10 F

Midterm Review

5/13 M

Midterm

5/15 W

5.1

Eigenvectors and Eigenvalues

5/17 F

5.2

The Characteristic Equation

5/20 M

5.3

Diagonalization

5/22 W

5.4

Eigenvectors and Linear Transformations

5/24 F

5.5

Complex Eigenvalues

5/29 W

6.1

Inner Product, Length and Orthogonality

5/31 F

6.2

Orthogonal Sets

6/03 M

6.3

Orthogonal Projections

6/05 W

6.4

The Gram-Schmidt Process

6/07 F

Final Review

Final Exam

Final Exam: Monday, June 10, 10:30 a.m. - 12:30 p.m..

Homework Problems:

HW 1: Due Tuesday 4/9
Sec. 1.1: 1, 2, 8, 9, 12, 13, 15, 18, 23, 24
Sec. 1.2: 1, 2, 10, 11, 12, 15, 16, 17, 18, 29, 31

HW 2: Due Tuesday 4/16
Sec. 1.3: 1, 2, 5, 6, 7, 10, 11, 14, 19, 20, 23, 24
Sec. 1.4: 2, 3, 6, 8, 9, 12, 14, 15, 22
Sec. 1.5: 1, 3, 5, 7, 12, 13, 15, 17, 20

HW 3: Due Tuesday 4/23
Sec. 1.7: 2, 3, 6, 7, 10, 12, 19, 20, 21, 22, 39
Sec. 1.8: 1, 2, 3, 5, 8, 9, 11, 17, 20, 21
Sec. 1.9: 2, 3, 5, 11, 17, 23, 25, 29, 30

HW 4: Due Tuesday 4/30
Sec. 2.1: 1, 4, 8, 9, 16, 17, 18, 27
Sec. 2.2: 1, 4, 5, 7, 8, 9, 13, 14, 18, 24, 29 ,32
Sec. 2.3: 4, 5, 8

HW 5: Due Tuesday 5/7
Sec. 2.3: 11, 12, 13, 15, 22, 23
Sec. 2.8: 3, 5, 8, 10, 11, 13, 16, 18, 21, 24, 27
Sec. 2.9: 1, 2, 5, 6, 9, 12, 13, 17, 19

HW 6: Due Tuesday 5/14
Sec. 3.1: 2, 6, 7, 12, 13, 15, 16, 19, 22, 40
Sec. 3.2: 1, 2, 3, 4, 6, 8, 13, 23, 24, 27, 31, 34

HW 7: Due Thursday 5/23
Sec. 3.3: 5, 14, 17, 18, 19, 24
Sec. 5.1: 1, 2, 3, 6, 11, 12, 16, 18, 21, 23
Sec. 5.2: 4, 5, 9, 12, 16, 19, 20

HW 8: Due Thursday 5/30
Sec. 5.3: 2, 3, 6, 7, 8, 11, 16, 21, 25, 31
Sec. 5.4: 1, 2, 5, 9, 12, 15, 17, 20, 23

HW 9: Due Thursday 6/6
Sec. 5.5: 4, 5, 7, 10, 16
Sec. 6.1: 1, 6, 7, 9, 10, 13, 19, 20, 22
Sec. 6.2: 3, 5, 8, 12, 13, 24, 27

Lecture	Date	Section	Topic
1	4/01 M	1.1	Systems of Linear Equations
2	4/03 W	1.2	Row Reduction and Echelon Forms
3	4/05 F	1.3	Vector Equations
4	4/08 M	1.4	The Matrix Equation Ax=b
5	4/10 W	1.5	Solution Sets of Linear Systems
6	4/12 F	1.7	Linear Independence
7	4/15 M	1.8	Introduction to Linear Transformations
8	4/17 W	1.9	The Matrix of a Linear Transformation
9	4/19 F	2.1	Matrix Operations
10	4/22 M	2.2	The Inverse of a Matrix
11	4/24 W	2.3	Characterizations of Invertible Matrices
12	4/26 F	2.8	Subspaces of R^n
13	4/29 M	2.8, 2.9	Continued
14	5/01 W	2.9	Dimension and Rank
15	5/03 F	3.1	Introduction to Determinants
16	5/06 M	3.2	Properties of Determinants
17	5/08 W	3.3	Cramer's Rule, Volume and Linear Transformations
18	5/10 F		Midterm Review
19	5/13 M		Midterm
20	5/15 W	5.1	Eigenvectors and Eigenvalues
21	5/17 F	5.2	The Characteristic Equation
22	5/20 M	5.3	Diagonalization
23	5/22 W	5.4	Eigenvectors and Linear Transformations
24	5/24 F	5.5	Complex Eigenvalues
25	5/29 W	6.1	Inner Product, Length and Orthogonality
26	5/31 F	6.2	Orthogonal Sets
27	6/03 M	6.3	Orthogonal Projections
28	6/05 W	6.4	The Gram-Schmidt Process
29	6/07 F		Final Review
			Final Exam