Consider the subspace S of ℝ⁴ given by S = {x ∈ ℝ⁴ : Ax = 0}, with A = [1 0 1 1; 1 1 0 1; 0 -1 1 1]. Find a basis for S, and show that it is indeed a basis.

a) {(1, 1, 0, 1), (0, -1, 1, 1)}
b) {(1, 0, 1, 1), (0, 1, -1, 1)}
c) {(1, 1, 1, 0), (1, 0, -1, 1)}
d) {(1, 1, 1, 1), (0, 1, 1, 1)}