. (a) Suppose W₁ and W₂ are subspaces in a vector space V and that V = W₁ + W₂. Prove that V = W₁ W₂ if and only if any vector v EV can be represented uniquely as v = v₁ + v2 where V₁ € W₁, V2 E W₂. = (b) Suppose W₁ and W₂ are subspaces in a vector space V, and such that V basis of W₁ and 32 is a basis of W2 prove that 3₁ U 32 is a basis of V. W₁ W₂. If B₁ is a

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