Determine e^(At) by first finding a fundamental matrix x(t) for x^(')=Ax and then using the formula e^(At)=x(t)x(0)^(-1).
A=[[4,1],[25,4]]
First, find x(t). Choose the correct answer below.
A. x(t)=[[-e^(-t),e^(9t)],[5e^(-t),5e^(9t)]]
B. x(t)=[[-e^(-t)cos9t,e^(9t)sin9t],[5e^(-t)cos9t,5e^(9t)sin9t]]
C. x(t)=[[(1-t)e^(-t),e^(9t)],[(5+1)e^(-t),5e^(9t)]]
D. x(t)=[[e^(-t),-e^(9t)],[5e^(-t),5e^(9t)]]
Next, find e^(At ).
e^(At)=
Determine eAt by first finding a fundamental matrix X(t) for x' = Ax and then using the formula eAt = X(t)X(O)- 1
First, find X(t). Choose the correct answer below
e-t cos 9t 9t sin 9t
OB.X(t)= 5e-t cos 9t 5e9t sin 9t
O c. X(t)=
OD.X(t)=
Next, find eAt