Hi everyone! Well, this is from my numerical analysis class, but we are starting with linear algebra and going from there, so I hope this is in the correct section.

Here's the question:

Suppose A has an LU factorization, where L is unit lower triangular and U is upper triangular. Is it possible that A has a factorization BC, where B is lower triangular and C is upper triangular, respectively. If so, how are these matrices related?

Reasoning: I have no idea where to start, but I am assuming that for a general case, then it would be possible. The LU factorization would be unique only if the diagonals consisted only of ones (i think) and that is not always the case, generally. If anyone could help I would really appreciate it.