Let A be a 4 x 4 matrix with the following characteristic polynomial: a) Find the eigenvalues of A. P(A) = 46A3 + 11λ² – 6A b) Find the geometric multiplicity of each eigenvalue. c) Determine the diagonalizability of A.

Let A be a 4 x 4 matrix with the following characteristic polynomial: a) Find the eigenvalues of A. P(A) = 46A3 + 11λ² – 6A b) Find the geometric multiplicity of each eigenvalue. c) Determine the diagonalizability of A.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 37EQ

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Question

Let A be a 4 x 4 matrix with the following characteristic polynomial:
a) Find the eigenvalues of A.
P(A) = 46A3 + 11λ² – 6A
b) Find the geometric multiplicity of each eigenvalue.
c) Determine the diagonalizability of A.

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