For these four problems determine if the given set W is a subspace of R³ .

Problem 1 Let W = {x E R3} satisfying the equation .rf = :2 + :3. Problem 2 Let W = {x E 1R3} satisfying the equation 3:12; 2 3:3. Problem 3 Let a, b be xed vectors in R3. and W = {x e R3} satisfying the equation x" a: a = 3:? a: b. Problem 4 Let W = {x E R3} satisfying the inequality 1, 2 2