I sometimes am a teaching assistant for MATH 133 at McGill, and introductory linear algebra course that covers linear systems, diagonalisation, geometry in two and three dimensional Euclidean space, and the vector space $ \mathbb{R}^n$, and I’ve collected a few theoretical questions here that I like to use in the hope that they may be useful to people studying this kind of material. I made up all of these questions, although obviously many of them in form are the same as elsewhere. Some of the questions are a bit unusual and curious, and none of them need special tricks to solve, just an understanding of the concepts in the course. They focus mostly on understanding the theory, and there are very few straight computational-type questions here.

*Note.* None of these questions are official in the sense that I do not write the final exams. The exact syllabus of the course should always be taken to be the class material and official course material on the course website. These are more for extra practice, but do cover the material of the course fairly closely.

More »