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
- Use elementary row operations to find the reduced row-echelon form of the augmented matrix of a system of linear equations and determine the solution set of the system.
- Find the equation of the span of a set of vectors in two- and three- dimensional real space and determine whether they are linearly independent.
- Be familiar with linear transformations and their standard matrices.
- Perform algebraic operations on matrices and find a basis for the row space, column space, and null space of a matrix and determine their dimensions.
- Evaluate the determinant of a matrix and be familiar with Cramer’s rule.
- Be familiar with the notions of orthogonality, length, and distance in an n -dimensional real space.
- Find the eigenvalues and eigenvectors of a given matrix and use them to diagonalize a matrix.
- 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).
Course topics
- Unit 1: Linear Systems of Equations
- Unit 2: Matrix Operations, Inverse, and Determinants
- Unit 3: Vector Spaces
- Unit 4: Dot Product and Cross Product
- Unit 5: Eigenvectors and Linear Transformations
Required text and materials
Students will have free access to materials directly within the course.
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 Written Assignment | 6% |
| Assignment 2: Unit 2 Written Assignment | 6% |
| Assignment 3: Unit 3 Written Assignment | 6% |
| Assignment 4: Unit 4 Written Assignment | 6% |
| Assignment 5: Unit 5 Written Assignment | 6% |
| WeBWorK (Assignments and Quizzes) | 30% |
| Mandatory Final Exam | 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.
