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ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. 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. sin (a) ə əx a Ω

Linear Algebra: A Modern Introduction
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 35EQ
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PLEASE ANSWER II) CORRECLTY

Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 A = 6-30 6-63 a) The characteristic polynomial is p(r) = det(A - rI) = (-(3-r)^2)(3+r) b) List all the eigenvalues of A separated by semicolons. 3;-3 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. ə ab sin (a) 8 a Ω 100 əx 0 f 3
Transcribed Image Text:Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 A = 6-30 6-63 a) The characteristic polynomial is p(r) = det(A - rI) = (-(3-r)^2)(3+r) b) List all the eigenvalues of A separated by semicolons. 3;-3 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. ə ab sin (a) 8 a Ω 100 əx 0 f 3
ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ∞ a Ω f əx ab sin (a) 0 P iii) If there is a third eigenvalue (the largest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ə ab sin (a) ∞ a Ω əx 0 P f E
Transcribed Image Text:ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ∞ a Ω f əx ab sin (a) 0 P iii) If there is a third eigenvalue (the largest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ə ab sin (a) ∞ a Ω əx 0 P f E
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