Suppose you wanted to make a cubic spline through the points (0,, 2), (2, 4), (4,16), (8, 12), and (12,8). a. write down the system of equations necessary to create a natural (free) cubic spline. b. solve your system using matlab, then write down the equation for the natural cubic spline. c. write down the system of equations necessary to create a clamped cubic spline, if the derivative at iso and the derivative at 12 is -1. d. solve your system using matlab, then write down the equation for the clamped cubic spline. e. write down the system of equations necessary to create a cubic spline with the "not-a-knot" conditions. f. solve your system using matlab, then write down the equation for the "not-a-knot" spline.