Consider the following nonhomogeneous system. X'= - - (-3-³) × + (-4²) Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) A2,-4 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.) K₁ = (1,-1) K₂ = (1,1) Find the general solution of the given system. 4 12 X(t) = C₁ (1,-1)e-2t. + c₂ (1₁1) €²¹² + ( 132,₁ ¹²2 ) ² + ( 8¹ 14 10 16 16 t + 98 64 14 64 X
Consider the following nonhomogeneous system. X'= - - (-3-³) × + (-4²) Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) A2,-4 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.) K₁ = (1,-1) K₂ = (1,1) Find the general solution of the given system. 4 12 X(t) = C₁ (1,-1)e-2t. + c₂ (1₁1) €²¹² + ( 132,₁ ¹²2 ) ² + ( 8¹ 14 10 16 16 t + 98 64 14 64 X
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:Consider the following nonhomogeneous system.
-1 3
x² - (-₁-³² ) x + (-4²²)
X' =
X
3-1
t+ 2,
Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.)
λ = 2,- 4
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.)
K₁
(1,-1)
(1,1)
K₂
=
Find the general solution of the given system.
4t
+ c₂(1,1)e4 +
X(t) = C₁ (1,-1)e-2t.
"
+
120 60 )₁ + (
14 10
16' 16
98
64'
14
64
X
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