Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 1 0 A = (¹9) 2 a) The characteristic polynomial is p(r) = det(A − rI) = r^2+2r+1 b) List all the eigenvalues of A separated by semicolons. 1;1 c) For each of the eigenvalues that you have found in (b) (from smallest to largest) give a basis of eigenvectors. If there is m than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there is only one eigenvalue, enter th zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eig ue. ə sin (a) əx B J a Ω AG X
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 1 0 A = (¹9) 2 a) The characteristic polynomial is p(r) = det(A − rI) = r^2+2r+1 b) List all the eigenvalues of A separated by semicolons. 1;1 c) For each of the eigenvalues that you have found in (b) (from smallest to largest) give a basis of eigenvectors. If there is m than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there is only one eigenvalue, enter th zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eig ue. ə sin (a) əx B J a Ω AG X
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 41EQ
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