n=U Problem 5. Let V be a vector space and W₁, W₂ be two subspaces of V. Define W₁ + W₂ = {x + y: x € W₁ and y € W₂}. (a) Prove that W₁ + W₂ is a subspace of V that contains both W₁ and W₂. (b) If W₁, W₂ are contained in the subspace W of V, then W₁ + W₂ is also contained in W. Problem 6. Let W = {(a₁, a2, a3) € R³ : a₁ = 3a2 and a3 = -a2}. Is W a subspace of R³ under the operations of addition and scalar multiplication defined on R³? Justify your answers.

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