Let A be an in x n matrix and let V be a subspace of R. (a)

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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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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 08:34 AM

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Let A be an in x n matrix and let V be a subspace of R. (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

Applied Linear Algebra

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