Please see attachment for full problem description and hint.
The solution of the vector-valued differential equation
dX/dt = AX(t) with X(0) = [a1
is given by:
X(t) = Exp(tA)X(0) = e^tA(X(0))
Explain how you would compute e^tA, and then find the general solution when:
A = [ 0 1 0
0 0 1
-1 1 1]
This solution calculates the characteristic of the matrix and finds all its eigenvalues.