Linked lists have nothing to do with matrices, as far as I know. And even if they did, it would be beyond idiotic to use them in that context.
And as Maritimo pointed out, we are not in the business of doing people's homeworks for them. We provide help in the form of explanations and hints to people who have shown genuine efforts towards solving the problem themselves.
As for matrix inversion and LU decomposition, I would suggest you just start with the wiki page on LU and the section on how to invert a matrix with it.