Some references for "Math 312: Linear Algebra"
This is a — probably available in your local library. They are very different from each other.
George Polya, How to Solve It, Princeton University Press (paperback)
Gilbert Strang, Linear Algebra and Its Applications, 4th Edition. A standard good text.
Strang has also taught an online version of his Linear Algebra course at MIT.
My own large collection of Linear Algebra Problems