Given subspaces H and K of a vector space V, the sum of H and K, written as H + K, is the set of all vectors in V that can be written as the sum of two vectors, one in H and the other in K; that is, H + K = {w : w =u + v for some u in H and some v in K} a. Show that H + K is a subspace of V. b. Show that H is a subspace of H + K and K is a subspace of H + K.

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A: Solution is given below

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