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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
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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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
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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