In Exercises 17–19, each of the given linear systems has zero as an eigenvalue. For each system, (a) find the eigenvalues; (b) find the eigenvectors; (c) sketch the phase portrait; (d) sketch the x(t)- and y(t)-graphs of the solution with initial condition Yo = (1, 0); %3D (e) find the general solution; and (f) find the particular solution for the initial condition Yo : your sketch from part (d). (1, 0) and compare it with n. - (:) -(:) -() dY 17. dt 4 2 Y 2 1 2 dY 18. dt 2 4 Y 3 6 dY 19. dt 0 -1

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 16EQ
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Can you please help me solve questions 17 and 19?

In Exercises 17–19, each of the given linear systems has zero as an eigenvalue. For
each system,
(a) find the eigenvalues;
(b) find the eigenvectors;
(c) sketch the phase portrait;
(d) sketch the x(t)- and y(t)-graphs of the solution with initial condition Yo = (1, 0);
(e) find the general solution; and
(f) find the particular solution for the initial condition Yo = (1, 0) and compare it with
your sketch from part (d).
1.- (:) -(G:) -()
dY
17.
dt
dY
18.
dt
2 4
Y
3 6
dY
19.
dt
4 2
Y
0 -1
2 1
Transcribed Image Text:In Exercises 17–19, each of the given linear systems has zero as an eigenvalue. For each system, (a) find the eigenvalues; (b) find the eigenvectors; (c) sketch the phase portrait; (d) sketch the x(t)- and y(t)-graphs of the solution with initial condition Yo = (1, 0); (e) find the general solution; and (f) find the particular solution for the initial condition Yo = (1, 0) and compare it with your sketch from part (d). 1.- (:) -(G:) -() dY 17. dt dY 18. dt 2 4 Y 3 6 dY 19. dt 4 2 Y 0 -1 2 1
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