Useful links:

Your course is based on Prof. Gil Strang's wonderful course at MIT. The current edition of 18.06 (MIT speak for linear algebra) lives here.

I strongly encourage you to check out the demos on the 18.06 page. These cover everything from matrix multiplication to singular value decomposition.

You can also view a complete semester's worth of lectures given by Prof. Strang in 2005 through MIT's OpenCourseWare.