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
- 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
The following materials are required for this course:
- Larson, R. (2017). Elementary linear algebra (8th ed.). Boston, MA: Brooks/Cole,
Cengage Learning.
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: 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.
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 exams@tru.ca with any questions.
| Assignment 1: Unit 1 | 9% |
| Assignment 2: Unit 2 | 9% |
| Assignment 3: Unit 3 | 9% |
| Assignment 4: Unit 4 | 9% |
| Assignment 5: Unit 5 | 9% |
| Quiz 1 | 7.5% |
| Quiz 2 | 7.5% |
| Final Exam (mandatory) | 40% |
| Total | 100% |
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.
