factor computes the LU factorization of the square,
non-singular argument matrix. It returns a list with 3 elements:
lu a matrix containing the LU factors
pvt a vector containing the pivot indices
rcond the reciprocal of the condition estimate
factor returns the results in the above format, so that they
may be conveniently used with backsub for repetitive
solutions. The lu function uses the results from
factor to produce separate L and U matrices.