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University of Waterloo · Waterloo · engineering
University of Waterloo MATH115 — Linear Algebra for Engineering
Start with linear systems, matrix operations and determinants, then review Euclidean vectors before the abstract and engineering applications in MATH115.
12 original question families · 36 parameter instances
Practise this course →Course alignment and coverage
2026–2027 Undergraduate Studies Academic Calendar, effective September 2026–August 2027, checked on 25 October 2026 through Waterloo’s public catalogue. A catalogue description is not a section syllabus.
Across this collection: 140 distinct original families and 420 parameter instances. Courses share topic banks; translations and shared mappings are not extra questions.
Supported learning objectives
Linear systems
Solve small two-variable systems, count a free variable and identify a singular parameter.
Matrix calculations
Compute selected sum/product entries, 2×2 determinants and an inverse entry.
Euclidean vectors
Calculate dot products, lengths, distances and a projection coefficient in two or three dimensions.
What is not covered
Selected small-system, matrix-entry and Euclidean-vector calculations only. No full row-reduction workspace, abstract vector-space proofs, eigenvalues, diagonalization, complex arithmetic, cross products, or line/plane equation exercises.
An original worked example
Solve x+y=5 and x-y=-1. Enter x only.
Worked solution
Answer: 2
- 2x=4.
- Thus x=2 and y=3; both original equations hold.
Official course sources
Independent, original, free self-study practice. Not affiliated with or endorsed by this university; these are not official exam questions. Topic alignment does not establish transfer credit, a current section’s weekly syllabus, full course coverage or a grade prediction. Follow your instructor’s rules and use official course materials for assessed work. No live AI chat or paid access is required.