Linear Algebra really does depend on what kind of thinker you are. If you're able to "picture" things not easily pictured, it all collapses down quite straight-forwardly in the end. It is very much about understanding - once you actually understand what is happening, you'll notice the course just repeats itself... (You'll do a bunch of stuff with the vectors you know - n-tuples, and come back to do the same things with general vector spaces - take polynomials as vectors, take matrices as vectors, etc. Scary things like "kernels" and "images" are things you learnt in week 1, etc.)
Except for the proofs. They've give you something that you go "duh, of course that's true", and have no idea how to begin an actual proof.

Full disclosure: I really liked Linear Algebra (compared with Calculus 2). My marks reflected that.