a. Given the points (1,0), (3,8), (6,5), and (10,-1), analytically derive the system of equations for the natural cubic splines that interpolate them. Explicitly write the system of equation in matrix form, you can exclude the coefficients that are already known, but be extremely careful with the calculations as it's very easy to make a mistake.

b. Solve the system of equations using MATLAB's backslash function and plot the points as well as the cubic splines. Provide code and plots.