9Which subspaces are the same for these matrices of different sizes?(a) [A] and[^]Α(b)AА[A] and [AA]Prove 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 [A] (b) [A] A A and A A Prove that all three of those matrices have the same rank r.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 25EQ

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Question

9
Which subspaces are the same for these matrices of different sizes?
(a) [A] and
[^]
Α
(b)
A
А
[A] and [AA]
Prove that all three of those matrices have the same rank r.

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