Question: Let U and V be finite-dimensional vector spaces. (a) Find a formula for dim( U V) in terms of dim U and dim V.

Let U and V be finite-dimensional vector spaces.
(a) Find a formula for dim( U × V) in terms of dim U and dim V. (See Exercise 49 in Section 6. 1.)
(b) If W is a subspace of V, show that dim Δ = dim W, where Δ = {(w, w): w is in W}.

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