U of T · MAT223
Linear Algebra I
Vectors, matrices, and transformations — taught so they actually make sense.
About this course
MAT223 is the standard first-year linear algebra course at U of T. It covers systems of linear equations, matrix algebra, determinants, vector spaces, and linear transformations.
Most students learn the mechanical steps (row reduction, finding eigenvalues) without understanding what they mean geometrically or conceptually. This makes the course fragile — a small variation on a familiar problem and you're lost.
We teach linear algebra the right way: connecting the algebra to the geometry, showing why the definitions are what they are, and building the kind of flexible understanding that holds up on every exam question.
Weekly review sessions run throughout the semester. Individual tutoring also available.
Topics covered
- Systems of linear equations and row reduction
- Matrix operations and invertibility
- Determinants and their geometric meaning
- Vector spaces and subspaces
- Linear independence, span, and basis
- Linear transformations and their matrix representations
- Eigenvalues and eigenvectors
- Orthogonality and projections
What you get
Concept-first sessions
We make sure you understand what every operation means, not just how to execute it.
Exam prep
Targeted review sessions timed to midterms and finals.
Problem-solving strategy
How to approach unfamiliar questions systematically.
Ready to get started?
Book a free diagnostic session and find the right starting point.
