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Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 6-30 6-63 a) The characteristic polynomial is A = 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. b sin (a) ə əx 8 a Ω

Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 6-30 6-63 a) The characteristic polynomial is A = 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. b sin (a) ə əx 8 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 38EQ
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PLEASE ANSWER II) CORRECTLY, I HAVE TRIED, [0,0,0] AND [0,1,1] AND [0,0,1] AND [(0,1,1),(0,0,1)] AND ALL ARE WRONG. IF U PUT ONE OF THE WRONG ANSWERS I WILL DISLIKE

ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ab sin (a) 0 ab 0 f əx sin (a) ə iii) If there is a third eigenvalue (the largest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. əx ∞ f a ∞ Ω E a Ω P P
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. ab sin (a) 0 ab 0 f əx sin (a) ə iii) If there is a third eigenvalue (the largest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. əx ∞ f a ∞ Ω E a Ω P P
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 6-30 6-63 a) The characteristic polynomial is A = 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. ab 0 sin (a) ə əx f 8 a Ω 100 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 6-30 6-63 a) The characteristic polynomial is A = 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. ab 0 sin (a) ə əx f 8 a Ω 100 3
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