The vectors were  <0,0,0,1>, \ <0,0,2,1>, \ <0,3,2,1>, \ <0,1,-1,1> .

It should be  A^{T} from post #3. But  \det A = \det A^{T} = 0 . So they are linearly dependent. But I think the problem hes having is that he keeps get the trivial solution.

Do RREF, as Jhevon said.