The math problem we address is:
Let A, , , , be matrices of compatible size be given. Solve , , , , and for a, b, c and for , , and . When can they be solved? If these equations can be solved, find formulas for the solution.
We shall make the strong assumption that each is invertible. While this assumption turns out to be valid, making it at this point is cheating. Ironically, we recommend strongly that the user make heavy invertibility assumptions at the outset of a session. Later, after the main ideas have been discovered, the user can selectively relax them and thereby obtain more general results.