MATH 204: Matrix & Vector Fundamentals Before Your First Exam
Work through systems, row operations, dot products and linear independence with original examples and checks for Concordia MATH 204.
Subject area
CEGEP Linear Algebra Tutoring
Connect linear systems, matrices and vectors in Québec Science linear algebra. Learn to interpret a calculation geometrically instead of treating row operations as isolated rules.
Topics covered
Linear equations and systemsRow operations and solution setsMatrix arithmeticVectors and dot productsLines and planesIntersections and geometric interpretation
Common difficulties
- Keeping an augmented column aligned with the variables
- Recognizing a free variable rather than forcing a unique solution
- Distinguishing a point, direction vector and normal vector
How tutoring can help
A system is a set of constraints. We connect each row operation to preserving that solution set, then interpret the result as intersecting lines or planes. Vector exercises start with a labelled sketch and the geometric question: direction, perpendicularity, distance or intersection.
Current codes and earlier search terms
These are subject crosswalks for the Science program, not transfer-credit decisions. The prefix matters: 201-SN1 is probability and statistics, while 203-SN1 is mechanics. Local codes and scope vary; your current outline is the reference.
| Subject | Current code | Earlier term |
|---|---|---|
| Linear algebra and vector geometry | 201-SN4-RE | 201-NYC-05 |
Check current names and content in the official Dawson mathematics list and Dawson physics list.
An example that connects the ideas
The system x + y = 3 and 2x + 2y = 6 describes the same line twice. Subtracting twice the first row from the second gives 0 = 0: infinitely many solutions, (x,y) = (3 − t,t). If the second right-hand side were 7, elimination would give 0 = 1: no solution.
A question to check understanding
Does (2,1) satisfy both original equations? Yes. A row-reduction result should survive substitution into the original system.
An original Nablio example. Independent support, with no college affiliation.
Independent practice
Free resources to work through
Exam preparation
Book a LessonReview with a clear plan.
Include systems with one, infinitely many and no solutions. Verify a proposed point in every original equation. For vector geometry, state what a parameter represents and test whether an answer satisfies the line or plane before moving on.
Courses by institution
Restrictions and confirm-first courses are marked on each page.