Consider the system 71=-1+2i dt where x is a 2 × 1 vector. a) Find the eigenvalues r₁, 72 and the corresponding eigenvectors. ✓ T2=-1-2 i The eigenvectors are -1+2i ¹-(13) * X -5 1 dx ✓ X and -1-2 i 1 X b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. The origin is a saddle point X and is asymptotically stable ✓ ✓ c) Sketch, by hand (without using any graphing device), several trajectories in the phase plane. d) Use an appropriate graphing device to plot accurately several trajectories in the phase plane and the corresponding graphs of ₁ versus t and 2 versus t.

Consider the system 71=-1+2i dt where x is a 2 × 1 vector. a) Find the eigenvalues r₁, 72 and the corresponding eigenvectors. ✓ T2=-1-2 i The eigenvectors are -1+2i ¹-(13) * X -5 1 dx ✓ X and -1-2 i 1 X b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. The origin is a saddle point X and is asymptotically stable ✓ ✓ c) Sketch, by hand (without using any graphing device), several trajectories in the phase plane. d) Use an appropriate graphing device to plot accurately several trajectories in the phase plane and the corresponding graphs of ₁ versus t and 2 versus t.

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 27EQ

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