Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 A = 4-2 4 0 0 3 a) The characteristic polynomial is p(r) = det(A - rI): b) List all the eigenvalues of A separated by semicolons. 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 the unneeded answer fields below. i) Give a basis of eigenvectors associate to the smallest eigenvalue. ab 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.

Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 3 0 0 A = 4-2 4 0 0 3 a) The characteristic polynomial is p(r) = det(A - rI): b) List all the eigenvalues of A separated by semicolons. 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 the unneeded answer fields below. i) Give a basis of eigenvectors associate to the smallest eigenvalue. ab 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.

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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