Let A be an m x n matrix of rank r. Suppose v1,. . . vn are

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Let A be an m x n matrix of rank r. Suppose v1,. . . vn are a basis for Rn such that vr+1.......vn form a basis for ker A. Prove that w1 = Av1.... . wr = Avr, form a basis for mg 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 m x n matrix of rank r. Suppose v1,. . . vn are

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Since we know dim rngA r it suffices to prove that w 1 w r are linearly independent Given 0 ...View the full answer

Applied Linear Algebra

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