After 10 years of teaching middle school, I am going back to grad school in math. I haven't seen Linear Algebra in more than a decade, but my first class is on Generalized Inverses of Matrices (what am I thinking?). I have a general "rememberance" understanding of most of the concepts we're discussing, but I get lost on where to start with proofs and such (teaching at such a low level for so long has really rotted my brain). Anyway, we were asked to find the orthogonal projection matrix from R^3 to the xy-plane. I understand geometrically what we're being asked to do, but I do not know where to start. If anyone could give me an idea, that would be great.