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Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -3 A = 4 2 a) The characteristic polynomial is p(r) = det(ArI) = b) List all the eigenvalues of A separated by semicolons. -3;4 c) For each of the eigenvalues that you have found in (b) (in increasing order) 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 is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. sin (a) a Ω f əx X

Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -3 A = 4 2 a) The characteristic polynomial is p(r) = det(ArI) = b) List all the eigenvalues of A separated by semicolons. -3;4 c) For each of the eigenvalues that you have found in (b) (in increasing order) 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 is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. sin (a) a Ω f əx X

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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ii) If there is another eigenvalue, give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. sin (a) ∞ a f əx P
Transcribed Image Text:ii) If there is another eigenvalue, give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. sin (a) ∞ a f əx P
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -3 0 ₁-(₁9) A = -21 4 2 a) The characteristic polynomial is p(r) = det(A — rI) = b) List all the eigenvalues of A separated by semicolons. -3;4 c) For each of the eigenvalues that you have found in (b) (in increasing order) 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 is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. ə ab sin (a) ∞ a əx f a Ω
Transcribed Image Text:Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -3 0 ₁-(₁9) A = -21 4 2 a) The characteristic polynomial is p(r) = det(A — rI) = b) List all the eigenvalues of A separated by semicolons. -3;4 c) For each of the eigenvalues that you have found in (b) (in increasing order) 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 is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. ə ab sin (a) ∞ a əx f a Ω
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