Please provide detailed solution for III part asap to get a upvote b)Let A, BE M(R) be two square matrices.i) Explain what it means that the matrices A nnd B are similar, i.e., A~ B.ii) Prove that if the matrices A and B are similar, then the the characteristic polyno-mial of the matrix A equals to the characteristic polynomial of the matrix B, i.e.,PA(:) = Pa(2).iii) Give an example of two matrices A, B e M2,2(C) such thatA) A is not similar to B; andB) pA(:) = PA(2).Give a detailed justification to your answer.

Answered: Image /qna-images/answer/486a20d0-27f1-4d1d-b6de-6823bbbfecc8.jpg

Answered: iii) Give an example of two matrices A,…

iii) Give an example of two matrices A, BE M22(C) such that A) A is not similar to B; and B) PA(:) = PA(:). Give a detailed justification to your answer.

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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Please provide detailed solution for III part asap to get a upvote

b)
Let A, BE M(R) be two square matrices.
i) Explain what it means that the matrices A nnd B are similar, i.e., A~ B.
ii) Prove that if the matrices A and B are similar, then the the characteristic polyno-
mial of the matrix A equals to the characteristic polynomial of the matrix B, i.e.,
PA(:) = Pa(2).
iii) Give an example of two matrices A, B e M2,2(C) such that
A) A is not similar to B; and
B) pA(:) = PA(2).
Give a detailed justification to your answer.

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