## Mathematics 252

### Linear Algebra

Length of Course: 14 weeks

Classroom Hours per Week: 4

Number of Credits: 3

Prerequisite: 12 credits

Corequisite: Mathematics 114

### Course Description:

An introduction to linear algebra including theory and application of vector spaces, linear transformations and matrices, eigenvectors and eigenvalues and inner product spaces.

### Course Outline:

Length Description

Week 1

Systems and Linear Equations and Matrices: Introduction to systems of linear equations, Gaussian elimination

Week 2

Systems and Linear Equations and Matrices: Matrices and matrix operations, Inverse matrix, properties of matrices

Week 3

Systems and Linear Equations and Matrices: Elementary matrices, Methods of finding inverse matrix, More on linear systems and invertible matrices, Applications

Week 4

Determinants: Determinants by cofactor expansion, evaluating determinants by row reduction

Week 5

Determinants: Properties of determinants, Cramer’s rule

Week 6

Euclidean Vector Spaces: Vectors in 2,3 and n-space, Norm, Dot product, Distance, Orthogonality, Cross product

Week 7

General Vector Spaces: Real vector spaces, Subspaces, Linear independence, Coordinates and basis

Week 8

General Vector Spaces: Dimension, Change of basis

Week 9

General Vector Spaces: Row space, Column, space, Null space, Rank, Nullity

Linear Transformations: General linear transformations

Week 10

General Vector Spaces: Matrix transformation from Rn  to Rm

Eigenvalues and Eigenvectors: Definition and computation of eigenvalues, eigenvectors, and eigenspaces

Week 11

Eigenvalues and Eigenvectors: Diagonalization

Week 12

Inner Product Spaces: Inner products, Orthogonality, Gram-Schmidt process

Week 13

Review

Week 14

Final Exam

### Textbook

Elementary Linear Algebra, Howard Anton, latest edition

### Course Evaluation:

10-20% Quizzes and Homework Midterm Exam(s) Final Exam

### Instructors

Arman Ahmadieh B.Sc., M.Sc. (Sharif University of Technology)
Hayri Ardal, B.Sc.(Bogazici), Ph.D.(Simon Fraser)
Kim Peu Chew, B.Sc. (Nanjing), M.A., Ph.D. (British Columbia)