Thanks for the answers to my initial question about matrices. Let me refine it further. I would like your comments about the wisdom of including matrices in first or second year algebra. I know that calculators can solve equations using them, but it seems that students are just button-pushers and don't understand WHY it works. (maybe that doesn't matter?). I also am concerned about the time this topic takes from the other parts of the course.
For myself, I am more comfortable with the model of using matrices as a topic in an elective higher-end course.