Let V = R³ with the usual vector addition, but with scalar multiplication given by k(a, b, c) = (ka, kb, k²c) for (a, b, c) € R³ and k € R. Is V a vector space? Let V = R4 with the usual operations. S = {(a, b, c, d) EV:a-2b + 3d=0}. Is S a subspace of V?

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