Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -3 A = a) The characteristic polynomial is p(r) = det(A - rI) = (r+3)(r-4) b) List all the eigenvalues of A separated by semicolons. -3;4 c) For each of the eigenvalues that you have found in (b) (in increasing order) 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 is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. Ə b sin (a) 8 a Ω əx f E
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -3 A = a) The characteristic polynomial is p(r) = det(A - rI) = (r+3)(r-4) b) List all the eigenvalues of A separated by semicolons. -3;4 c) For each of the eigenvalues that you have found in (b) (in increasing order) 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 is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. Ə b sin (a) 8 a Ω əx f E
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:ii) If there is another eigenvalue, give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector.
ab sin (a)
∞
a
f
dx
a
AZ
Transcribed Image Text:Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix
-3
0
^= (-2)
A
9).
a) The characteristic polynomial is
p(r) = det(A - rI) = (r+3)(r-4)
b) List all the eigenvalues of A separated by semicolons.
-3;4
c) For each of the eigenvalues that you have found in (b) (in increasing order) 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 is only one eigenvalue, enter the zero
vector as an answer for the second eigenvalue.
i) Give a basis of eigenvectors associated to the smallest eigenvalue.
ab
sin (a)
∞
a
ii) If there is another eigenvalue, give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector.
08
f
C
X
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