Question

Does the method LU Decomposition to solve for unknowns in a system of equation only work for \[Ax=b\] when there is only one solution \[x\]? Would it still help to find the whole subspace of the solution set if the matrix happens to have free variables?

Answer 1

There are a number of cases where a singular matrix is not LU factorisable..

http://arxiv.org/abs/math.NA/0506382

Answer 2

thank you, polpak! :)