For the system of differential equations, - -9 1 _3] x + [ -¹ + ] y 8 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. A1, A2 = U1 = y' U2 = -7 = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter the eigenvectors as a matrix with an appropriate size. 6
For the system of differential equations, - -9 1 _3] x + [ -¹ + ] y 8 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. A1, A2 = U1 = y' U2 = -7 = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter the eigenvectors as a matrix with an appropriate size. 6
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![For the system of differential equations,
[]+[4]
y
6 8
a) Find the characteristic polynomial of the matrix of coefficients A.
CA(X)
A1, A2 =
U₁ =
=
b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order
separated by commas.
U₂ =
c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller
eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter
the eigenvectors as a matrix with an appropriate size.
v(t)
y'
=
d) Determine a general solution to the system by completing the following steps.
i. Find v(t) = = [y−¹(t)f(t)dt .
yp(t) =
-7
y (t)
ii. Find a particular solution y(t).
=
ii. Then a general solution for the system in the matrix form is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2323f944-68c6-4ffb-b4bd-7709a3866c17%2Fad73343e-62c1-4b21-adad-327456742095%2F9zrc2ui_processed.png&w=3840&q=75)
Transcribed Image Text:For the system of differential equations,
[]+[4]
y
6 8
a) Find the characteristic polynomial of the matrix of coefficients A.
CA(X)
A1, A2 =
U₁ =
=
b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order
separated by commas.
U₂ =
c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller
eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter
the eigenvectors as a matrix with an appropriate size.
v(t)
y'
=
d) Determine a general solution to the system by completing the following steps.
i. Find v(t) = = [y−¹(t)f(t)dt .
yp(t) =
-7
y (t)
ii. Find a particular solution y(t).
=
ii. Then a general solution for the system in the matrix form is
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