Consider the set S = (v₁ = (1,0,0), v₂ = (0, 1,0), v3 = (0, 0, 1), v4 = (1, 1,0), vs = (1, 1, 1)). a) Give a subset of vectors from this set that is linearly independent but does not span R³. Explain why your answer works. b) Give a subset of vectors from this set that spans R³ but is not linearly independent. Explain why your answer works.