1. Linear Transformations: the following ask you to work with the two defining properties of linear transformations. (a) Show that D, defined as D(y(t) ) = y(t) + p(t )y(t), is is a linear transformation. (b) Show that I, defined as 1 (g (t)) = / 9(t) at, is a linear transformation. If the input is g(#), describe the kinds of functions that are outputs of I(g(t)). (c) Show that C, defined as C(f(t)) = e-si f (t ) dt , is a linear transformation. If the input is f(t), describe the kinds of functions that are outputs of C(f(t)) - specifically, identify the independent variable for the output function