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(Solved): Ask an expert Problem 1 For the matrix A=[[5,2],[1,4]] : a. find the eigenvalues \lambda _(i); b. fi ...
Ask an expert Problem 1 For the matrix A=[[5,2],[1,4]] :
a. find the eigenvalues \lambda _(i);
b. find corresponding eigenvectors vec(v)_(i);
c. neatly sketch the phase portrait for the ODE
(d(vec(Y)))/((d)t)=Avec(Y)
using a ruler. Please include arrows on solution curves in your phase portraits to il-
lustrate the direction of flow, and be sure to include all straight-line solutions on your
graph, plus a 'representative' number of other solutions; and then
d. find the particular solution to the IVP
(d(vec(Y)))/((d)t)=Avec(Y)
with initial condition vec(Y)(0)=[[3]]
0.
Problem 2 Repeat problem 1a-d for the matrix A=[[1,3],[3,1]] and initial condition
vec(Y)(0)=[[2],[0]]