Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 30 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.
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 30 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.
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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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)
a
Ω
f
əx
8
AZ
Transcribed Image Text: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) =
80
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)
∞
Ω
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.
E
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