Time invariance is where the output is not effected by time. As the book puts it the behavior and characteristics of the system are fixed over time.
Time Invariant Problem
Time Variant Problem
(Time variant problem was taken from the in class "exercise" section I posted)
$ Y(t) = x(t - 1) - x(1 - t) $
$ S_1 = Y(t) = x(t - 1) - x(1 - t) $
$ S_2 = Y(t) = x(t - t_o) $
$ x(t) -> S1 -> S2 -> x(t - t_o - 1) - x(1 - t + t_o) $
$ x(t) -> S2 -> S1 -> x(t - t_o - 1) - x(1 - t - t_o) $
$ x(t - t_o - 1) - x(1 - t + t_o) =/= x(t - t_o - 1) - x(1 - t - t_o) $
