Students explore the following topics: systems of linear equations, matrix arithmetic,
determinants, real vector spaces, linear transformations, eigenvalues, eigenvectors, and
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
- 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
- Larson, R. Elementary linear algebra. 8th edition. Boston, MA: Brooks/Cole, Cengage
Textbook ISBN: 978-1-305-65800-4
- 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
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, students are responsible for the fee to the online proctoring service, ProctorU, or to the in person approved Testing Centre. Please contact firstname.lastname@example.org 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
|Assignment 2: Unit 2
|Assignment 3: Unit 3
|Assignment 4: Unit 4
|Assignment 5: Unit 5
|Final examination *
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.