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Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -17 -32 16 3 3 3 4 43 -8 A = 9 9 -40 9 -52 53 9 9 9 a) The characteristic polynomial is p(r) = det(ArI) = 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 answer fields that are not needed. i) Give a basis of eigenvectors associated to the smallest eigenvalue: b sin (a) ə əx ∞ α Ω a ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. b sin (a) ə əx a Ω ܨܩܕ a E C

Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -17 -32 16 3 3 3 4 43 -8 A = 9 9 -40 9 -52 53 9 9 9 a) The characteristic polynomial is p(r) = det(ArI) = 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 answer fields that are not needed. i) Give a basis of eigenvectors associated to the smallest eigenvalue: b sin (a) ə əx ∞ α Ω a ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. b sin (a) ə əx a Ω ܨܩܕ a E C

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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iii) If there is a third eigenvalue (the largest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ab sin (a) ∞ Ω f əx Pi 8
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. ab sin (a) ∞ Ω f əx Pi 8
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -17 -32 16 3 3 43 -8 9 9 -40 -52 53 9 9 9 a) The characteristic polynomial is p(r) = det(A — rI) = b) List all the eigenvalues of A separated by semicolons. 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 answer fields that are not needed. i) Give a basis of eigenvectors associated to the smallest eigenvalue: ab sin (a) Ω f əx ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ab sin (a) ∞ Ω f əx ܗܘ ܪܐܣܘ ܝ 8 8 2 E AZI Pi
Transcribed Image Text:Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -17 -32 16 3 3 43 -8 9 9 -40 -52 53 9 9 9 a) The characteristic polynomial is p(r) = det(A — rI) = b) List all the eigenvalues of A separated by semicolons. 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 answer fields that are not needed. i) Give a basis of eigenvectors associated to the smallest eigenvalue: ab sin (a) Ω f əx ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ab sin (a) ∞ Ω f əx ܗܘ ܪܐܣܘ ܝ 8 8 2 E AZI Pi
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