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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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