Consider the following nonhomogeneous system. (Enter any column vector as a row vector.) 3 x' = x + -4t2 t + 3, Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) λ = 4,-2 You got it! Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue. If there is only one repeated eigenvalue, enter the eigenvector in each answer blank.) Κι = (-1,1) K₂ (1,1) That's right! You're right! Find the general solution of the given system. x(t)=C₁-1,1)e 2¸ 4t - C₂(1,1)e¹² +

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.3: The Exponential Distribution
Problem 3P
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Consider the following nonhomogeneous system. (Enter any column vector as a row vector.)
3
x' =
x +
-4t2
t + 3,
Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.)
λ = 4,-2
You got it!
Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue. If there is only one repeated eigenvalue, enter the
eigenvector in each answer blank.)
Κι
=
(-1,1)
K₂
(1,1)
That's right!
You're right!
Find the general solution of the given system.
x(t)=C₁-1,1)e 2¸
4t
- C₂(1,1)e¹² +
Transcribed Image Text:Consider the following nonhomogeneous system. (Enter any column vector as a row vector.) 3 x' = x + -4t2 t + 3, Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) λ = 4,-2 You got it! Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue. If there is only one repeated eigenvalue, enter the eigenvector in each answer blank.) Κι = (-1,1) K₂ (1,1) That's right! You're right! Find the general solution of the given system. x(t)=C₁-1,1)e 2¸ 4t - C₂(1,1)e¹² +
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