I know that in order to show an equivalence relation I need to check for (1) reflexivity, (2) Symmetry, and (3) transitivity. I just cant figure out how to prove those things for this problem. (Problem attached.) 7. Let M be the set of all n x n matrices. Define a relation on ~ on M byA B there exists an invertible matrix P such that A = PBP.Show that is an equivalence relation.

Answered: 7. Let M be the set of all n x n…

7. Let M be the set of all n x n matrices. Define a relation on ~ on M by A B there exists an invertible matrix P such that A = P BP. Show that ~ is an equivalence relation.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

I know that in order to show an equivalence relation I need to check for (1) reflexivity, (2) Symmetry, and (3) transitivity. I just cant figure out how to prove those things for this problem. (Problem attached.)

7. Let M be the set of all n x n matrices. Define a relation on ~ on M by
A B there exists an invertible matrix P such that A = PBP.
Show that is an equivalence relation.

Expert Solution

Step 1

A relation ~ is said to be an equivalent relation if it hold following three properties

(1) reflexivity, (2) Symmetry, and (3) transitivity

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Solved in 4 steps with 3 images

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