Exercises 29–34 require knowledge of the sum and direct sum of subspaces, as defined in the exercises of Section 1.3.
(a) Find an example of subspaces W1 and W2 of R3 with dimensions m and n, where m > n > 0, such that dim(W1 ∩ W2) = n.
(b) Find an example of subspaces W1 and W2 of R3 with dimensions m and n, where m > n > 0, such that dim(W1 + W2) = m + n.
Find an example of subspaces W1 and W2 of R3 with dimensions m and n, where m ≥ n, such that both dim(W1 ∩ W2) < n and dim(W1 + W2) < m + n.
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