Subject area
Online CEGEP Linear Algebra Tutoring
Tutoring in linear systems, matrices and vector geometry for Québec CEGEP Science programs. Connect row operations to solution sets and interpret systems as lines or planes.
Start with a concept you would like explained or a question you do not yet know how to begin. A course outline or an attempted solution can help if you have one. We confirm the level, topics and availability before booking. Tutoring sessions are currently offered in English. In-person options in Montréal
Courses by institution
Go directly to examples and revision for your course. Each institution guide explains the other courses and their differences; follow your section’s outline and announced chapters.
Choose an institution to browse courses in this subject. You can also text or email us directly.
Browse courses in this subjectTopics covered
Linear equations and systemsRow operations and solution setsMatrix arithmeticVectors and dot productsLines and planesIntersections and geometric interpretation
Common difficulties
- Keeping the variable columns and right-hand-side column in the correct order
- Recognizing a free variable instead of forcing a unique solution
- Distinguishing a point, a direction vector and a normal vector
How tutoring can help
Your tutor can follow your row operations and use a small geometric example to explain why the solution set is preserved. For vector problems, you can connect your calculation to the diagram and identify whether the difficulty concerns direction, perpendicularity, distance or an intersection.
Current and former course codes
This table matches current and former codes by Science program subject. Your institution must confirm any transfer-credit equivalence. The prefix matters: 201-SN1 is probability and statistics, while 203-SN1 is mechanics. Course codes and topics can vary by institution. Check your current course outline.
| Subject | Current code | Former code |
|---|---|---|
| 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.
Worked example
The system and describes the same line twice. Subtracting twice the first row from the second gives : infinitely many solutions, , where is any real number. If the second right-hand side were 7, elimination would give : no solution.
Check your understanding
Does satisfy both original equations? Yes. A row-reduction result should survive substitution into the original system.
Review systems and vector geometry for CEGEP
Begin with systems or vector geometry, depending on the question you need to solve. These shared lessons were written for university courses; choose only the topics and methods in your current CEGEP outline. This is a focused revision route, not a full course.
- Explain why row operations keep the same solutions
Use reversible operations, read each final row as an equation, and decide whether the system has one, no or infinitely many solutions. Check your result in the original equations.
- Connect dot products and projections to a sketch
Use the vector diagram to distinguish a scalar dot product from a vector projection. This Concordia MATH 204 lesson includes shared vector topics; attempt the self-checks that match your CEGEP work.
At each step: read the example, attempt a question before opening its solution, then redo a missed step without notes. Finish by applying the method to permitted practice from your own course.
Independent practice
Free study guides and practice
Matrices and Vectors: Practice for Concordia MATH 204
Practise systems, row operations, dot products and linear independence with original worked examples and self-checks for Concordia MATH 204.
Exam preparation
Book a LessonWhat to practise
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.
Need help in another CEGEP subject? Explore CEGEP math and physics tutoring.