Exercises 29–34 require knowledge of the sum and direct sum of subspaces, as defined in the exercises of Section 1.3.
Let W1 and W2 be subspaces of a vector space V having dimensions m and n, respectively, where m ≥ n.
(a) Prove that dim(W1 ∩ W2) ≤ n.
(b) Prove that dim(W1 + W2) ≤ m + n.
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