# MATH 2121: Linear Algebra

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

## Learning outcomes

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 topics

• 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

## 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.

## Assessments

Please be aware that should your course have a final exam, you are responsible for the fee to the online proctoring service, ProctorU, or to the in-person approved Testing Centre. Please contact exams@tru.ca with any questions about this.

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

## Open Learning Faculty Member Information

An Open Learning Faculty Member is available to assist students. Students will receive the necessary contact information at the start of the course.

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