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 .b I(9 (t) ) = / 9(t ) at , is a linear transformation. If the input is g(t), describe the kinds of functions that are outputs of I(g(t)). (c) Show that L, defined as L(f (t) ) = e-st f ( t ) at , 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