Consider the following simultaneous linear differential equations. dx = -x + 2y, dy dt = = 3y. dt (a) Express the system of equations in matrix form.

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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Consider the following simultaneous linear differential equations.
dx
dy
= -x+2y,
= 3y.
dt
dt
(a) Express the system of equations in matrix form.
(b) Find the eigenvalues and eigenvectors of the matrix of coefficients.
(c) Hence write down the general solution to this system.
Transcribed Image Text:Consider the following simultaneous linear differential equations. dx dy = -x+2y, = 3y. dt dt (a) Express the system of equations in matrix form. (b) Find the eigenvalues and eigenvectors of the matrix of coefficients. (c) Hence write down the general solution to this system.
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