James Cook's Introduction to Linear Algebra Page
James Cook's Linear Algebra Homepage:

Welcome. This webpage contains many resources I have created for linear algebra.

General Advice: When confronting many "proof" problems in this course (and in more advanced abstract math courses) as a starting point you ought to ask yourself:
1. What am I asked to prove ?
2. Can I define the words used ?
It is not usually the case that you will find the same proof in my notes or some text. Definitions are key, I cannot emphasize this enough. Past this, you should consider using theorems, propositions etc. which we have developed. However, beware of proof by synonym. A common beginners mistake is to simply restate the claim in slightly different words as to prove the claim by invoking an entirely equivalent theorem. I usually write an arrow pointing back to itself to warn you of the circularity of such logic. Anyway, enough about what not to do, you can learn what is a good method of proof simply by following lectures and paying mind to study the structure of our arguments in each lecture. We do solve problems in this course, but, our more over-arching goal is to understand the structure of linear algebra.

Lectures from previous semesters:

This course is similar in spirit to previous offerings, however, I am making several significant modifications in format.
1. The websites linked below provide various matrix calculations online:
2. Previous versions of my notes are found below. Note, these are from the time when Math 221 was not a prerequisite for Math 321. The notes from 2024 and beyond have a significant rewrite.
3. The solutions below are from a previous semester.
4. An interesting example: the mapping T(A)=BAB has rank 4 despite the fact B has rank 2. See this row reduction which is in response to Part 2 of Lecture 20 of Linear Algebra 2015.
Spring 2015 Course Materials:
The content of 2016 and 2015 is more or less identical, however, I follow a somewhat different path. In particular, I have structured the quizzes to cover material in series rather than in parallel with the major tests. In any event, there is still value in last year's Lectures, but, I do hope this year is an improvement.

Spring 2015 Lectures, Quiz and Test Solutions:
Spring 2015 Lectures:

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