Find the general solution to the following system of linear differential equations. The independent variable is t. All of the eigenvalues and one of the eigenvectors are provided. 2x₁ + 2x₂ + 4x3 = 2x₁ -x₁ + x₂ = 2x₂ + x3 x3 = 2x₁ + x₂ + x3 2₁ = 1, 2₂1, 23 = 4 = -(-²) -2 K₂ =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Find the general solution to the following system of linear differential equations. The independent variable is t.
All of the eigenvalues and one of the eigenvectors are provided.
2x₁ + 2x₂ + 4x3 = 2x₁
-x₁ + x₂ = 2x₂ + x3
x3 = 2x₁ + x₂ + x3
2₁ = 1, 2₂1, 23 = 4
=
-(-²)
-2
K₂ =
Transcribed Image Text:Find the general solution to the following system of linear differential equations. The independent variable is t. All of the eigenvalues and one of the eigenvectors are provided. 2x₁ + 2x₂ + 4x3 = 2x₁ -x₁ + x₂ = 2x₂ + x3 x3 = 2x₁ + x₂ + x3 2₁ = 1, 2₂1, 23 = 4 = -(-²) -2 K₂ =
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