Let W1 and W2 be subspaces of a vector space V. Let W1 + W2 be the

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Let W1 and W2 be subspaces of a vector space V. Let W1 + W2 be the set of all vectors v in V such that v = w1 + w2, where w1 is in W1 and w2 is in W2. Show that W1 + W2 is a subspace of V.
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