I need help with these questions:

i.Let L = {(1, 2, 1, 3),(0, 0, 1, 1)}. Let G = {v₁ = (1, 2, 2, 0), v₂ = (1, 0, 0, 1), v₃ = (0, 1, 1, 1), v₄ = (1, 2, 2, 4)}. You can assume without proof that G spans R⁴ . Find two vectors in G that can be replaced by the two elements of L in such a way that the spanning property is preserved.

ii.Prove that if W₁ and W₂ are finite-dimensional subspaces of a vector space V, then the subspace W₁ + W₂ is finite-dimensional, and dim(W₁ + W₂) = dim(W₁) + dim(W₂) -dim(W₁ W₂). Hint: Start with a basis {u₁, u₂ , ... , u_k} for W₁ W₂ and extend this set to a basis {u₁, u₂ , ... , u_k, v₁, v₂ , ... , v_m} for W₁ and to a basis {u₁, u₂ , ... , u_k, w₁, w₂ , ... , w_p} for W₂.