Elementary Linear Algebra

The best textbook I've used for Linear Algebra! It has just the right theoretical aspect and fills you with a lot of examples (A LOT). It's perfect if you have an engineering mindset in which you want to apply the theories and patterns to solve real-world problems.
One con is the solutions to exercises are short and usually just the results without any further discussions.

This is a generally good introduction for engineers/scientists, but I think Gilbert Strang's text is still far stronger and far better for those of almost any background.