Let A = 9 -6 0 9 -6 0 4 5 3 eigenspace. (a) Compute the characteristic polynomial pë(λ). (b) Use your answer from part (a) to find all the eigenvalues of A. (c) For each eigenvalue from part (b), find a basis of the corresponding eigenspace. (d) Use your answer from part (c) to determine whether A is diagonalizable. If so, produce an invertible matrix P and a diagonal matrix D such that A = PDP ¹. If not, explain why not in a complete sentence.

Let A = 9 -6 0 9 -6 0 4 5 3 eigenspace. (a) Compute the characteristic polynomial pë(λ). (b) Use your answer from part (a) to find all the eigenvalues of A. (c) For each eigenvalue from part (b), find a basis of the corresponding eigenspace. (d) Use your answer from part (c) to determine whether A is diagonalizable. If so, produce an invertible matrix P and a diagonal matrix D such that A = PDP ¹. If not, explain why not in a complete sentence.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section: Chapter Questions

Problem 9RQ

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