j Recall that Mnxn (R) is the vector space of n x n matrices with real coef- ficients. Let A and B be two given n x n matrices such that B is invertible. Is the set {X € Mnxn (R) | AXB-¹ = X} a vector space? Justify your answer.

j Recall that Mnxn (R) is the vector space of n x n matrices with real coef- ficients. Let A and B be two given n x n matrices such that B is invertible. Is the set {X € Mnxn (R) | AXB-¹ = X} a vector space? Justify your answer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 63EQ

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j
Recall that Mnxn (R) is the vector space of n x n matrices with real coef-
ficients. Let A and B be two given n x n matrices such that B is invertible. Is the
set
{X € Mnxn (R) | AXB-¹ = X}
a vector space? Justify your answer.

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