show all steps to the solution Let A be a non-zero matrix that is diagonalizable. Show that A" # 0, for any positive integer r.0 for some positive integer k.Definition: A nilpotent matrix is a square matrix M such that Mnilpotent matrices are not diagoanalizable.)0 1Show that 0 0001 is not diagonalizable.0Show that a non-zero n x n upper triangular matrix with zero diagonal entries is not diagonalizable.

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Let A be a non-zero matrix that is diagonalizable. Show that A" # 0, for any positive integer r. Definition: A nilpotent matrix is a square matrix M such that M = 0 for some positive integer k. nilpotent matrices are not diagoanalizable. 0 1 Show that 0 0 1 is not diagonalizable. 0 00 Show that a non-zero n x n upper triangular matrix with zero diagonal entries is not diagonalizable.

Let A be a non-zero matrix that is diagonalizable. Show that A" # 0, for any positive integer r. Definition: A nilpotent matrix is a square matrix M such that M = 0 for some positive integer k. nilpotent matrices are not diagoanalizable. 0 1 Show that 0 0 1 is not diagonalizable. 0 00 Show that a non-zero n x n upper triangular matrix with zero diagonal entries is not diagonalizable.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 41EQ: In general, it is difficult to show that two matrices are similar. However, if two similar matrices...

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