Let A be an in x n matrix and let V be a subspace of R. (a)
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(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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a First W rng A since every w W can be written as w Av for ...View the full answer
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