## Linear differential equation system with periodic coefficients AND periodic solutions

Hello!

I have a linear differential equation system with periodic coefficients:

x'(t) = A(t) x(t)
x(0) = known

where x'(t) is dx(t)/dt, A(t) a periodic matrix: A(t+T) = A(t) with T the period.

How must be A(t) (conditions to be accomplished) if I want x(t) to be periodic as well? x(t+T) = x(t).

Thank you very much!