Let A, BE MInn(R) be two square matrices. i) Explain what it means that the matrices A and 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(:). iii) Give an example of two matrices A, BE M2.2(C) such that A) A is not similar to B; and B) PA(:) = PA(:). Give a detailed justification to your answer. %3D
Let A, BE MInn(R) be two square matrices. i) Explain what it means that the matrices A and 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(:). iii) Give an example of two matrices A, BE M2.2(C) such that A) A is not similar to B; and B) PA(:) = PA(:). Give a detailed justification to your answer. %3D
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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Transcribed Image Text: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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