Let V be a vector space over a field F and let W1 and W2 be subspaces of V. Define the sum of W1 and W2 by W1 +W2 = {wi + w2 | w1 E W1 and w2 E W2}. (a) Show that W1 +W2 is a subspace of V. (b) Let B1 be a basis for W1 and B2 be a basis for W2. Show that B1 U B2 is a basis for W1 +W2 if and only if W1 N W2 = {0}. %3D

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