MATH 2121

Linear Algebra

Description

Students explore the following topics: systems of linear equations, matrix arithmetic, determinants, real vector spaces, linear transformations, eigenvalues, eigenvectors, and diagonalization.

Delivery Methods

Online, self-paced.

Recommended Requisites

Test MA12 - Pre-calculus 12 or MATH 0633 or MATH 1001 or MATH 1141

MATH 2120

Objectives

Upon successful completion of the course, students should be able to:

• Solve systems of linear equations and homogeneous systems of linear equations by Gaussian elimination and Gauss-Jordan elimination.
• Row-reduce a matrix to either row-echelon or reduced row-echelon form.
• Use matrix operations to solve systems of equations and be able to determine the nature of the solutions.
• Understand some applications of systems of linear equations.
• Perform operations with matrices and find the transpose and inverse of a matrix.
• Calculate determinants using row operations, column operations and expansion down any column and across any row.
• Interpret vectors in two and three-dimensional space both algebraically and geometrically.
• Use the Gram-Schmidt process to produce an orthonormal basis.
• Use basic mathematical proof techniques to prove or disprove certain claims (e.g. prove or disprove whether a given set of objects constitutes a vector space).
• Find the kernel, range, rank, and nullity of a linear transformation.
• Calculate eigenvalues and their corresponding eigenspaces.
• Understand the concept of a linear transformation as a mapping from one vector space to another and be able to calculate its matrix representation with respect to standard and nonstandard bases.
• Determine if a matrix is diagonalizable, and if it is, how to diagonalize it.

Course Outline

• Unit 1: Systems of Linear Equations
• Unit 2: Matrices and Determinants
• Unit 3: Vector Spaces
• Unit 4: Inner Product Spaces
• Unit 5: Linear Transformations, Eigenvalues and Eigenvectors

30 weeks.

Required Text and Materials

1. Larson, R. Elementary linear algebra. 8th edition. Boston, MA: Brooks/Cole, Cengage Learning, 2017.
Textbook ISBN: 978-1-305-65800-4
1. Larson, R. Student solutions manual for elementary linear algebra. 8th edition. Boston, MA: Brooks/Cole, Cengage Learning, 2017.
Textbook ISBN: 978-1-305-65802-8

Optional Materials

A scientific calculator is allowed both in the course term work and on the final exam. Graphing calculators are not permitted.

Open Learning Faculty Member

An Open Learning Faculty Member is available to assist students. Primary communication is through the Learning Environment’s “Mail” tool or by phone. Students will receive the necessary contact information at the start of the course.

Assessments

To successfully complete this course, students must achieve a passing grade of 50% or higher on the overall course, and 50% or higher on the final mandatory examination.

 Assignment 1: Unit 1 8% Assignment 2: Unit 2 8% Assignment 3: Unit 3 8% Assignment 4: Unit 4 8% Assignment 5: Unit 5 8% Final examination * 60% Total 100%

* Mandatory