# riceissa comments on What exercises go best with 3 blue 1 brown’s Linear Algebra videos?

• Some other sources of exercises you might want to check out (that have solutions and that I have used at least partly):

• Multiple choice quizzes (the ones related to linear algebra are determinants, elementary matrices, inner product spaces, linear algebra, linear systems, linear transformations, matrices, and vector spaces)

• Vipul Naik’s quizzes (disclosure: I am friends with Vipul and also do contract work for him)

Regarding Axler’s book (since it has been mentioned in this thread): there are several “levels” of linear algebra, and Axler’s book is at a higher level (emphasis on abstract vector spaces and coordinate-free ways of doing things) than the 3Blue1Brown videos (more concrete, working in ). Axler’s book also assumes that the reader has had exposure to the lower level material (e.g. he does not talk about row reduction and elementary matrices). So I’m not sure I would recommend it to someone starting out trying to learn the basics of linear algebra.

Gratuitous remarks:

• I think different resources covering material in a different order and using different terminology is in some sense a feature, not a bug, because it allows one to look at the subject from different perspectives. For instance, the “done right” in Axler’s book comes from one such change in perspective.

• I find that learning mathematics well takes an unintuitively long time; it might be unrealistic to expect to learn the material well unless one puts in a lot of effort.

• I think there is a case to be made for the importance of struggling in learning (disclosure: I am the author of the page).

• To add a little on different terminologies being a feature: if you ultimately want to apply linear algebra, you’ll have to build a bridge from the theory to the particular application that is probably even more difficult than the bridge between two presentations of the theory. So it’s probably good to practice building bridges.

(I’m also suspicious of people who say that the last book that they read on a subject was the best book, because that’s when it clicked. How much did the first books prepare them?)

• That does make sense.