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.