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

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 54E

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