Let A be an n n matrix. (a) Show that A2 = 0 if and only

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Let A be an n × n matrix.
(a) Show that A2 = 0 if and only if col A ⊆ null A.
(b) Conclude that if A2 = 0, then rank A ≤ n/2.
(c) Find a matrix A for which col A = nullA.

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Linear Algebra With Applications

ISBN: 9780070985100

7th Edition

Authors: W. Keith Nicholson

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Question Posted: Jun 21, 2016 06:39 AM

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Let A be an n n matrix. (a) Show that A2 = 0 if and only

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b If A 2 0 then AAx 0 for all xin R n that is Ax X ...View the full answer

Linear Algebra With Applications

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