Question: 2. Let V be a vector space: Ha a subspace of V, and suppose that V/I'V is nite-dimensional. a) Let Q: V > V/W be

2. Let V be a vector space: Ha\" a subspace of V, and suppose that V/I'V is nite-dimensional. a) Let Q: V > V/W be the quotient map. Prove that there exists a linear map 3 : V/H'" > V such that Q3 : I. b) Prove that V is isomorphic to the product 1vector space W x V/W. (Hint. Show that the map 1: > ((I SQX'U), Q09) is an isomorphism, where S is your map constructed in a).) [10]

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