Let u v sub w be subspaces of a finite dimensional vector
Let U, V ⊂ W be subspaces of a finite dimensional vector space W . Define U + V = {w ∈ W | w = u + v, u ∈ U, v ∈ V }.
(a) Prove that dim(U + V ) ≤ dim U + dim V .
(b) Give an example where the inequality in (a) is strict.
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