Question: Let V and W be finitedimensional vector spaces. Define the direct product V X W of V and W to be the Cartesian product V

Let V and W be finitedimensional vector spaces. Define the direct product V X W of V and W to be the Cartesian product V X W (as a set) endowed with addition (01,100+ (02, W2) = (01 + 02, L01 + W2) and scalar multiplication c - (v, w) = (cv, cw). (a) Prove that with these operations, V X W becomes a vector space. (b) Prove that V x W = (V x {0}) GB ({0} x W). (e) What does (b) imply about dim V X W

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