2. 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 (Li, Yi). Output the polynomial coefficients for the two splines S.2) and S (2). 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 (Az = b) using the command x = A/b to get your coefficients. (b) Apply your function from (a) to the set of points. Give the cubic splines, S. (C) and Si(2), 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. 2. 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 (Li, Yi). Output the polynomial coefficients for the two splines S.2) and S (2). 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 (Az = b) using the command x = A/b to get your coefficients. (b) Apply your function from (a) to the set of points. Give the cubic splines, S. (C) and Si(2), 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