I just found this set of lecture notes on linear algebra which seems to go over several things I've been wondering about as I study linear algebra. Unfortunately there are very few exercises in the text and I'm not even positive I have the skill to prove the first few lemmas myself. I have read the first couple of sections so far, and I think I understand the material as well I as can while not having any exercises to practice on -- which is not well enough. So my question is:
Is there a book/ reference which goes over this same material, but can be more easily self-studied? Or else can anyone recommend a text which will at least prepare me enough to be able to figure these lecture notes out on my own?