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 2013-06-01, )
ATTENTION:
For information about the textbook, please consult with the assigned instructor for details.
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Introduction to Linear Algebra, 5th 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 6.4 Symmetric matrices. Time Permitting 6.5 Positive definite matrices.