Consider that matrix A 12 24-2 36-3 (a) Find the eigenvalues of A. Also find the corresponding eigenspaces and their dimensions. (b) Explain why A is diagonalizable. Calculate A2021 (c) Your friend claims "I think if P diagonalizes A, then P diagonalizes every integral power of A." Is his statement correct? If not, under what condition(s) the statement holds true? Can you prove it in general?

Consider that matrix A 12 24-2 36-3 (a) Find the eigenvalues of A. Also find the corresponding eigenspaces and their dimensions. (b) Explain why A is diagonalizable. Calculate A2021 (c) Your friend claims "I think if P diagonalizes A, then P diagonalizes every integral power of A." Is his statement correct? If not, under what condition(s) the statement holds true? Can you prove it in general?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8BEXP

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