QEDmath

It sounds like you're taking an intro linear algebra course which focuses on row operations to solve systems of equations and all the stuff that goes with it. The interesting theoretical stuff happens when you start going into linear operators on a vector space (take a look at Sheldon Axler's "Linear Algebra Done Right"). Maybe this will spark some interest.

Wear a black shirt. Black hides massive pit stains very well.

Try checking higheredjobs.com. Community colleges always have a large pool of adjuncts on hand; send some emails with CV's, etc. I took an adjunct position after getting my MA (in mathematics) while I was deciding about research areas for a PhD. I credit my teaching experience as an adjunct as one thing that may have set me apart from other applicants. Good luck reapplying and getting some adjunct positions (you'll need a few to survive!).

The same with me. Keeping my fingers (and toes) crossed for funding.