Question: Let A be an in x n matrix and let V be a subspace of R. (a) Show that W = AV = { A

Let A be an in x n matrix and let V be a subspace of R".
(a) Show that W = AV = { A v | v € V } forms a subspace of rng A.
(b) If dim V = k, show that dim W ≤ min{k, r}, where r = rank A.

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