MATH 235 W24 - A2 Question 1 Only parts d), e), f) and g) will be marked. Consider the following subsets of V = C° (R). Determine whether they are vector

subspaces or not. If the subset is a subspace of C (R), then write YES, and prove that it is. If the subset is not a subspace of C (R), then write NO, and prove that it is not. (a) W₁ = {g(x) € V : g(0) + g(1) = 1}. (b) W₂ = {g(x) = V : g(0) + g(1) = 0}. (c) W3 = {g(x) € V: (g(0)) (g(1)) = 0}. (d) W₁ = {g(x) € V : g(x) + (d(g(x))) = 1}. (e) W₁ = {g(x) € V : g(x) + (d(g(¹))). = 0}. = {9(a) € V : (g(x)) (d(g(x))) = 0}. (f) W6 = (g) W7 = {g(x) = V : (g(x)) (d(g(x)) - 1) 2 (d(g(x))) + 3 (F² (g(x))) = 0}. 3 ( 1¹² (q(7))) = 2²}. 2 (d(g(x))). +3 (h) Ws = {g(x) € V : g(x) + 2 (i) W₂ = {g(x) € V: g(x) + 2 = = 0}.