1. Consider the following linear systems of ordinary differential equations: (a) dx/dt = 3x – 2y, dy/dt = 2x – 2y %3D (b) dr/dt = x – 5y, dy/dt = x - 3y %3D For each of the system: (i) Find the eigenvalues and eigenvectors of each linear system. (ii) Classify the critical point (0, 0) as to type, and determine whether it is stable, asymptotically stable, or unstable.

1. Consider the following linear systems of ordinary differential equations: (a) dx/dt = 3x – 2y, dy/dt = 2x – 2y %3D (b) dr/dt = x – 5y, dy/dt = x - 3y %3D For each of the system: (i) Find the eigenvalues and eigenvectors of each linear system. (ii) Classify the critical point (0, 0) as to type, and determine whether it is stable, asymptotically stable, or unstable.

Name: 1 1. Consider the following linear systems of ordinary differential eq
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Description: 1 1. Consider the following linear systems of ordinary differential equations:(a) dx/dt = 3x – 2y,dy/dt = 2x – 2y(b) dx/dt= x - 5y,dy/dt = x – 3yFor each of the system:(i) Find the eigenvalues and eigenvectors of each linear system.(ii) Classify the

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

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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