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1. Solve the following systems of equations by matrix method (solving the eigenvalue problem). In each case, find the equilibrium point(s). Finally, sketch the phase portrait by hand in a way that clearly shows the relationship between the (directed) trajectories and the direction of eigenvectors, and any possible rotational effects, and determine the behavior (source, sink, or saddle) and type (asymptotically stable, or unstable) of the equilibrium point(s). i = 4x + 5y (a) 1) * - ( )* Si = -2r1 - 12 (c) |i2 = x1 – 4x2 3 2 (b) х = -x + 2y 8. -3 0 (& ) 1 3 (d) x = (e) x = 3 9 -3

1. Solve the following systems of equations by matrix method (solving the eigenvalue problem). In each case, find the equilibrium point(s). Finally, sketch the phase portrait by hand in a way that clearly shows the relationship between the (directed) trajectories and the direction of eigenvectors, and any possible rotational effects, and determine the behavior (source, sink, or saddle) and type (asymptotically stable, or unstable) of the equilibrium point(s). i = 4x + 5y (a) 1) * - ( )* Si = -2r1 - 12 (c) |i2 = x1 – 4x2 3 2 (b) х = -x + 2y 8. -3 0 (& ) 1 3 (d) x = (e) x = 3 9 -3

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 6EQ
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need Help with problems A and B! Only complete solutions to A and B please. Thank you.
1. Solve the following systems of equations by matrix method (solving the eigenvalue problem). In each case, find the equilibrium point(s). Finally, sketch the phase portrait by hand in a way that clearly shows the relationship between the (directed) trajectories and the direction of eigenvectors, and any possible rotational effects, and determine the behavior (source, sink, or saddle) and type (asymptotically stable, or unstable) of the equilibrium point(s). i = 4x + 5y (a) Sa = -2x1 – 12 (c) |i2 = 11 – 4x2 3 2 (b) х = -x + 2y 8. -3 (& ) 1 3 -3 0 (d) x = (e) x = 3 9 -3
Transcribed Image Text:1. Solve the following systems of equations by matrix method (solving the eigenvalue problem). In each case, find the equilibrium point(s). Finally, sketch the phase portrait by hand in a way that clearly shows the relationship between the (directed) trajectories and the direction of eigenvectors, and any possible rotational effects, and determine the behavior (source, sink, or saddle) and type (asymptotically stable, or unstable) of the equilibrium point(s). i = 4x + 5y (a) Sa = -2x1 – 12 (c) |i2 = 11 – 4x2 3 2 (b) х = -x + 2y 8. -3 (& ) 1 3 -3 0 (d) x = (e) x = 3 9 -3
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