For the system of differential equations, 6 - 5 18 16 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 = 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 X₂. Enter the eigenvectors as a matrix with an appropriate size. U2 = y' = y(t) d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂. = C1 + c₂
For the system of differential equations, 6 - 5 18 16 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 = 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 X₂. Enter the eigenvectors as a matrix with an appropriate size. U2 = y' = y(t) d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂. = C1 + c₂
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 35EQ
Related questions
Question
![For the system of differential equations,
a) Find the characteristic polynomial of the matrix of coefficients A.
CA(X)
=
A1, A2 =
y'
U1 =
=
b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order
separated by commas.
U2 =
- 5
6
18 16
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 X₂. Enter
the eigenvectors as a matrix with an appropriate size.
d) Determine a general solution to the system.
Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂.
y(t) = C1
+ c₂](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2323f944-68c6-4ffb-b4bd-7709a3866c17%2F00d3b99a-8d9f-4ca9-b584-c6c80b8c43d5%2Fhcz8fcc_processed.png&w=3840&q=75)
Transcribed Image Text:For the system of differential equations,
a) Find the characteristic polynomial of the matrix of coefficients A.
CA(X)
=
A1, A2 =
y'
U1 =
=
b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order
separated by commas.
U2 =
- 5
6
18 16
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 X₂. Enter
the eigenvectors as a matrix with an appropriate size.
d) Determine a general solution to the system.
Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂.
y(t) = C1
+ c₂
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