1. The problem statement, all variables and given/known data Suppose you are given the LU factorization for some nxn square matrix A. Assume A is non-singular. This factorization is a result of partial pivoting. Can you use this factorization to solve A^Tx=b for x (given A and b). 2. Relevant equations A^T is the transpose of matrix A. PA = LU is the assumed factorization of A with partial pivoting Since P is a permutation matrix, P^T=P^-1 3. The attempt at a solution Haha...I figured it out... PA=LU A = (P^T)LU A^T = (U^T)(L^T)P A^Tx = (U^T)(L^T)Px = b Then let Px = y A^Tx = (U^T)(L^T)y = b U^T is then lower-triangular, L^T is unit-upper-triangular. Therefore I can solve for y in the usual way, and then figure out what x is based on the permutation matrix P.