In class, we have seen how to construct a new signal y(t) from an existing signal r(t) by time shift, time reversal and time scaling. Namely, y(t) = x(t to), or y(t) = x(-t), and y(t) = x(at). These time transformations can be considered as "systems" as well since it takes r(t) as input and outputs a signal y(t). Show that these three different time transformation systems are linear.