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(Solved): Let P=[[9,-4,-7]] 15, vec(y)_(1)(t)=[[2e^(3t)+4e^(-t)]] 3e^(3t)+10e^(-t),vec(y)_(2)(t)=[[-4e^(3t)+2 ...



Let

P=[[9,-4,-7]] 15, vec(y)_(1)(t)=[[2e^(3t)+4e^(-t)]] 3e^(3t)+10e^(-t),vec(y)_(2)(t)=[[-4e^(3t)+2e^(-t)]] -6e^(3t)+5e^(-t).

a. Show that

vec(y)_(1)(t)

is a solution to the system

vec(y)^(')=Pvec(y)

by evaluating derivatives and the matrix product

vec(y)_(1)^(')(t)=[[9,-4],[15,-7]]vec(y)_(1)(t)

Enter your answers in terms of the variable

t

.

[◻]=[[6e^(3t)-4e^(-t)],[9e^(3t)-10e^(-t)]]


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