Syllabus Detail

Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 22A: Linear Algebra

Approved: 2012-09-01 (revised 2026-05-06, E. Fuchs)
ATTENTION:
Actual textbook varies by instructor, please consult with the assigned instructor for details.
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Introduction to Linear Algebra, 6th Edition by Gilbert Strang; Wellesley Cambridge Press; $48.00-65.00.
Search by ISBN on Amazon: 978-0980232714
Prerequisites:
(MAT 016C C- or better or MAT 017C C- or better or MAT 021C C- or better or MAT 021CH C- or better); (ENG 006 or EME 005 or ECH 060 or MAT 022AL (can be concurrent)).
Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1

1.1

Vectors and linear combinations.

2

1.2

Lengths and dot products.

3

1.3

Matrices.

4

2.1

Vectors and linear equations.

5

2.2

The idea of elimination.

6

2.3

Elimination using matrices.

7

2.4

Rules for matrix operations.

8

2.5

Inverse matrices.

9

2.6

Elimination = Factorization: A = LU

10

2.7

Transposes and permutations.

11

3.1

Spaces and vectors.

12

3.2

Nullspace of A: Solving Ax = 0

13

3.3

The Rank and the Row Reduced Form

14

3.4

The complete solution to Ax = b

15

3.5

Independence, basis, and dimension.

16

3.6

Dimensions of the Four Subspaces.

17

4.1

Orthogonality of the Four Subspaces.

18

4.2

Projections.

19

4.3

Least squares approximations.

20

4.4

Orthogonal bases and Gram-Schmidt.

21

5.1

The properties of determinants.

22

5.2

Permutations and cofactors.

23

6.1

Introduction to eigenvalues.

24

6.2

Diagonalizing a matrix.

25

6.3

Symmetric matrices.

Time Permitting

6.5

Positive definite matrices.
Learning Goals:

The purpose of MAT 22A is to introduce students to the fundamental objects and concepts in Linear Algebra, supported by computations using MATLAB. At the conclusion of this course, students will be able to:

  • Compute and interpret matrix operations, including determinants, inverses, eigenvalues, and eigenvectors.
  • Solve systems of linear equations.
  • Find approximate solutions to systems of linear equations using least squares.
  • Perform computations on vector spaces, including computing bases, orthonormal bases, and eigenspaces.
  • Identify and interpret the four fundamental subspaces associated with a matrix.
  • Employ software tools (MATLAB) to solve large-scale or complex numerical problems
  • Apply linear algebra concepts to model, solve, and analyze real-world situations.

The "software tools" and the "applications" learning goal should be achieved by regularly featuring appropriate problems in lecture and discussion sections, and by consistently assigning problems involving applications and computer computations on homework. Resources for MATLAB lessons and examples can be found in Ali Daddel’s book on his Department-hosted webpage.

Examples of applications appropriate to cover in Math 22A can be found on Ali Dad-del's applications web page.