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N/Woor 0 A = -2 2-4 15 0 a) The characteristic polynomial is p(r) = det(A − rI) =

N/Woor 0 A = -2 2-4 15 0 a) The characteristic polynomial is p(r) = det(A − rI) =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 0 A = -2 2-4 3 0 2 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 as an answer in the extra boxes below. i) Give a basis of eigenvectors associated to the smallest eigenvalue. sin (a) ə əx ∞ Ω 3272 15 56 8 A₂
Transcribed Image Text:Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 0 A = -2 2-4 3 0 2 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 as an answer in the extra boxes below. i) Give a basis of eigenvectors associated to the smallest eigenvalue. sin (a) ə əx ∞ Ω 3272 15 56 8 A₂
iii) If there is a third eigenvalue (the largest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ə sin (a) ∞ Ω əx ܨܩ a f 8 ALI P
Transcribed Image Text:iii) If there is a third eigenvalue (the largest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ə sin (a) ∞ Ω əx ܨܩ a f 8 ALI P
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