Using Python:

In this problem, we'll do the LU decomposition. Again, you can type in the system at the top of the file. Write a function that takes and n times n invertible matrix A and returns matrices P, L and U so that A = PLU where P is a permutation matrix, L is lower trianglar with 1's on the diagonal and U is upper trianbular. Use scaled partial pivoting. Write a function that takes a vector b and uses the decomposition PLU to solve the system Ax = b using backward substitution and forward substituion. Store the matrics as numpy arrays