Students explore the following topics: systems of linear equations, matrix arithmetic,
determinants, real vector spaces, linear transformations, eigenvalues, eigenvectors, and
- 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
- 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
- Determine if a matrix is diagonalizable, and if it is, how to diagonalize it.
- 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
The following materials are required for this course:
- Larson, R. (2017). Elementary linear algebra (8th ed.). Boston, MA: Brooks/Cole,
Type: Textbook ISBN: 978-1-305-65800-4
- Larson, R. (2017). Student solutions manual for elementary linear algebra (8th
ed.). Boston, MA: Brooks/Cole, Cengage Learning.
Type: Textbook ISBN:
A scientific calculator is allowed both in the course term work and on the final exam.
Graphing calculators are not permitted.
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 email@example.com 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.
Note: The final exam for this course is only available as a in-person exam and must be
taken at an approved Testing Centre. Please email firstname.lastname@example.org with any questions.
|Assignment 1: Unit 1
|Assignment 2: Unit 2
|Assignment 3: Unit 3
|Assignment 4: Unit 4
|Assignment 5: Unit 5
|Final Exam (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.