PROBLEM 4: Given the data below. X 3.0 4.5 7.0 9.0 f(x) 2.5 1.0 2.5 0.5 a) By using Quadratic Spline Method, determine the 8 simultaneous equations used to form the matrix 4.5 1 0 0 20.25 1 0 C 0 0 49 0 0 O 0 14 1 0 b) Develop a program using excel sheet or any programming language of your choice to solve the unknowns of the matrix in (a) by applying any of the techniques of solving matrixes learned from previous lessons. (provide the code and screen shot of the results) To know that your program is correct the following results must be obtained. b, =-1 C1 - 5.5 a2 = 0.64 b2 =-6.76 C2 = 18.46 23 = -1.6 by = 24.6 C =-91.3 c) Use the result to derive the quadratic splines and estimate the value at x = 5.0