 # MAT 022A Linear Algebra

## Course Info

Matrices and linear transformations, determinants, eigenvalues, eigenvectors, diagonalization, factorization.

The purpose of MAT 22A is to introduce students to the fundamental objects and concepts in Linear Algebra, including scalars, vectors, matrices, diagonal matrices, symmetric matrices, inverse matrices, singular & nonsingular matrices, permutation matrices, linear combination, linear dependence & independence, vector spaces, subspaces, the dimension of a vector space, bases of vector spaces, rank, nullity, the four fundamental subspaces associated with a matrix, projections, determinants, permutations and cofactors, and eigenvectors & eigenvalues, and the fundamental operations on these objects including the dot product, matrix multiplication, matrix transpose, Gaussian elimination, Gauss-Jordon elimination, LU decomposition, matrix factorizations, reduction of a matrix to row reduced echelon form (RREF), the solution of systems of linear equations in an arbitrary number of unknowns, the least squares procedure and the Gram-Schmidt procedure. In MAT 22A a modern, innovative approach is taken in presenting this material. This approach gives students an introduction to logic and proof, which is one of the goals of this course.

## Course Files

August 5 August 6 August 7 August 8 August 9
What is Linear Algebra Gaussian Elimination & Row Operations Homework 1 Due Solution Sets & Vectors
Chapter 1
Notes
Sections 2.1, 2.3
Notes
Homework
Solutions
Sections 2.5, Chapter 4
Notes
August 12 August 13 August 14 August 15 August 16
Vector Spaces & Linear Transformations Homework 2 Due Midterm 1 Matrices & Their Properties
Chapters 5, 6
Notes
Homework
Solutions
Chapters 1-2, 4-6
Study Guide
Solutions
Extra Credit
EC Solutions
Sections 7.1, 7.3
Notes
August 19 August 20 August 21 August 22 August 23
Inverse Matrices & LU Decomposition Determinants Homework 3 Due Subspaces and Linear Independence
Sections 7.5, 7.7
Notes
Chapter 8
Notes
Homework
Solutions
Chapters 9, 10
Notes
August 26 August 27 August 28 August 29 August 30
Basis, Dimension, Kernel, Range, Nullity, & Rank Homework 4 Due Midterm 2 Eigenvalues & Eigenvectors, Diagonalization
Chapters 11, 16
Notes
Homework
Solutions
Chapters 7-11, 16
Study Guide
Solutions
Extra Credit
Chapters 12, 13
Notes
September 2 September 3 September 4 September 5 September 6
Labor Day Orthonormal Bases and Complements Homework 5 Due Symmetric Matrices and Least Squares
Chapter 14
Notes
Homework
Solutions
Chapters 15, 17
Notes
September 9 September 10 September 11 September 12 September 13
Singular Value Decomposition Homework 6 Due Review Day
The Simplex Method
Final Exam
Chapter 17
PCA Example
Notes
Homework
Solutions
Chapters 1-17
Notes
Chapters 1-2, 4-17
Study Guide