Consider the system of differential equations dx = x + 4y dt (Σ ) : dy 2x – y dt - (i) Write the system (E) in a matrix form.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Consider the system of differential equations
dx
= x + 4y
dt
(Σ ) :
dy
2. — у
dt
(i) Write the system (E) in a matrix form.
(ii) Find a vector solution by eigenvalues/eigenvectors.
(iii) Use the vector solution, write the solutions x(t) and y(t).
Transcribed Image Text:Consider the system of differential equations dx = x + 4y dt (Σ ) : dy 2. — у dt (i) Write the system (E) in a matrix form. (ii) Find a vector solution by eigenvalues/eigenvectors. (iii) Use the vector solution, write the solutions x(t) and y(t).
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