5. Using cubic spline interpolation, solve for the following using this set of data: X 2 8 10 a. Find matrix A b. Vector b C. Vector x f(x) 3 7 9

Given:

A set of data with x and f(x) values as follows: x f(x) 2 3 5 5 8 7 10 9

Task:

Use cubic spline interpolation to find the following: a. Matrix A b. Vector b c. Vector x

Expected Output:

a. Matrix A [[ 1. 0. 0. 0.]

                  [ 3. 12. 3. 0.]

                  [ 0. 3. 10. 2.]

                  [ 0. 0. 0. 1.]]

b. Vector b [0. 0. 1. 0.]

c. Vector x [ 0. -0.027027 0.1081081 0. ]