I just pushed an update to the Linear algebra explained in four pages tutorial.

Anyone who has an exam with lots of $A\vec{x}=\vec{b}$ stuff on it coming up should check it out because it covers: vector operations, matrix operations, linear transformations(matrix-vector product, fundamental vector spaces, matrix representation), solving systems of linear equations (the RREF stuff), matrix inverse, eigenvalues.

UPDATE: I found another excellent tutorial which I think you should also read, especially if you are a visual person. A Geometric Review of Linear Algebra by Prof. Eero P. Simoncelli (discuss on HN if you are a procrastinating person). If you’re a studious person, you’ll also go to en.wikibooks.org/wiki/Linear_Algebra and practice solving problems. To become a powerful person, don’t look at the solution until you’ve attempted the problem (with pen and paper) for at least five minutes.

UPDATE: I found some other useful short tutorials, like this short review of linear algebra from Stanford and another one from Boulder which both cover interesting details and bring a new perspective.