. Matrices A and B are said to be similar if and only if there is a matrix P such that A = PBP^-1 . If A and B are similar, show that 1) Det A = det B 2) A and B together have an inverse or do not have an inverse. 3) The characteristic equations of A and B are the same.
. Matrices A and B are said to be similar if and only if there is a matrix P such that A = PBP^-1 . If A and B are similar, show that 1) Det A = det B 2) A and B together have an inverse or do not have an inverse. 3) The characteristic equations of A and B are the same.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 11AEXP
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13. Matrices A and B are said to be similar if and only if there is a matrix P such that A = PBP^-1 . If A and B are similar, show that
1) Det A = det B
2) A and B together have an inverse or do not have an inverse.
3) The characteristic equations of A and B are the same.
4) The eigenvalues of A are the same as the eigenvalues of B.
5) The eigenvectors A and B can be different.
Please solve this problem complete please no reject
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