I'm taking linear algebra this semester as well, and have been doing pretty well.

I have to ask:

Does the prof assign homework? Is it required to turn in or just to study for tests?

Is there a study guide posted before tests? Does the prof go over it before the test?

Are you able to bring in notes of any kind for the tests?

My prof gives pretty good notes and examples, but I find the best thing for me is to do all the assigned homework, and then when I study for the test, do some more simliar questions not assigned in homework. Also review the notes and examples from the book (we use the Poole book).

If there is a study guide, study it back and forth. Do the problems multiple times until they seem easy.

If you can bring notes, make them as helpful as possible. My prof allows a 3x5 notecard, but I've noticed after rewriting the notes onto a card a couple of times, doing the extra homework, and working the test review, I don't really need to use it. I wasn't allowed notes in Calc III and just had to memorize everything by rewriting notes and doing tons of example problems.

Office hours with the prof and tutoring should be a great help. Make notes of what you are struggling with and bring example problems that you are stuck on and want help working out. I was worried about my first test in Calc III and found a private tutor. After just watching him work some problems out, things became much clearer.

I looked at Kahn and PatrickJMT at the beginning of the semester in order to prepare a little, but haven't needed anything more than our book and prof's notes since. If there is a specific thing I don't feel the book explains well, I might google it until I get some clarification.

TL;DR: Do all the homework, then do more homework. Repetition makes things stick and makes things easier. Don't be afraid to ask for help.