The usual proofs of the existence of **LU**-factorizations are done in
terms of elementary matrices. The Maple implementation below follows
the usual proofs closely (in fact, one can say that the structure of
the code * is* a proof for the decomposition --- in particular,
the * loop invariants* provide an inductive proof, given the properties
of elementary matrices).

Wed Jan 31 11:33:59 EST 1996