(2, 0), (3, —1), (5, 3). (a) Write a function for Natural Cubic Spline Interpolating Polynomials with only 3 points. Have as inputs two vectors, x and y, that give the 3 points (xi, yi). Output the polynomial coefficients for the two splines So(x) and S1(x).

. Consider the set of points:
(2, 0), (3, —1), (5, 3). (a) Write a function for Natural Cubic Spline Interpolating Polynomials with only 3 points. Have as inputs two vectors, x and y, that give the 3 points (xi, yi). Output the polynomial for the two splines So(x) and S1(x). Note: you do not need to implement the full algorithm in the book. Instead you can create a system of 8 equations with 8 unknowns and solve the linear system (Ax = b) using the command x = Alb to get your coefficients.
(b) Apply your function from (a) to the set of points. Give the cubic splines, So(x) and SI (x), in your write-up.
(c) Plot your splines found in (b) over the interval [2, 5] with step size 0.01 between points. Include the set of data points on the plot as well.