What books of completely solved problems (free in pdf) in linear algebra would you suggest?
Please suggest books that have solved problems, and not theory.
I really liked Strang's book for a well-rounded approach to the subject.
For sheer number of drill problems, Advanced Engineering Mathematics by Kreyszig has a section on linear algebra that's one of the better introductions I've seen. I use the 7th edition, which you can get very cheaply off Amazon.
There's also the abstract algebra book by Pinter, A Book of Abstract Algebra, that I recommend because it's easy to read and helps to keep the broader ideas in mind.
Ah! How about Schaum's Outlines of Linear Algebra? I think Paul Halmos' Problems Book of Linear Algebra work very well too.