Which subspaces are the same for these matrices of different sizes?Α(a) [A] and[A](b)[A][AA]and A AProve that all three of those matrices have the same rank r.

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Which subspaces are the same for these matrices of different sizes? (a) [A] and (b) [A] and [AA] [AA] Prove that all three of those matrices have the same rank r.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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Question

Which subspaces are the same for these matrices of different sizes?
Α
(a) [A] and
[A]
(b)
[A]
[AA]
and A A
Prove that all three of those matrices have the same rank r.

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Step 1: Rank of a matrix using row reduce.

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