Department of Mathematics, University of Toronto
MAT223H1F - Linear Algebra I
Suggestions for Review: Final Exam
The following is more of a review sheet for the material after Midterm II than it is one for the final exam. I
would suggest using the review sheets for the two midterm exams along with this one, as review sheets for
the final exam.
This may not cover every idea you need to master (not that I’m intentionally omitting something) but is
intended to identify and solidify the main points and connections between various concepts.
I suggest before you go through this document that you read through all your class notes and/or the text-
book and, as you’re reading, solve questions as you encounter a new topic. You should at least attempt to
solve all the computational style questions from the textbook, then some of the Find an Example questions
and some of the True or False questions. Once you’ve systematically worked through all the material from
the beginning, only then read this document.
Organizing and carrying out your own review is a critical
step to understanding and mastering new material. It is much more valuable than going through someone
else’s review. You should be able to state definitions precisely and make connections between various ideas.
You should be able to solve particular examples explaining you reasoning at every step. If you are doing
a proof and you are using a theorem to help complete the proof, you should state the theorem precisely.
Writing something like ”By Theorem in the textbook, yadda, yadda, yadda...” is not acceptable. You may
find working in small groups may worthwhile.
I hope this helps. Good Luck!