Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 A = 6 -3 0 6 -63 a) The characteristic polynomial is p(r) = det (A - rI) = b) List all the eigenvalues of A separated by semicolons. c) For each of the eigenvalues that you have found in (b) (working from smallest to largest) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there are fewer than three eigenvalues, enter the zero vector in any answer fields that are not needed. i) Give a basis of eigenvectors for the smallest eigenvalue. sin (a) Ə əx ∞ a Ω ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. f 1

Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 A = 6 -3 0 6 -63 a) The characteristic polynomial is p(r) = det (A - rI) = b) List all the eigenvalues of A separated by semicolons. c) For each of the eigenvalues that you have found in (b) (working from smallest to largest) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there are fewer than three eigenvalues, enter the zero vector in any answer fields that are not needed. i) Give a basis of eigenvectors for the smallest eigenvalue. sin (a) Ə əx ∞ a Ω ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. f 1

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.5: Iterative Methods For Computing Eigenvalues

Problem 42EQ

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