2. (8 points) Consider the piecewise cubic polynomial So(x), if 0 S(x)S( where Using the data points given in question 1., specify all twelve conditions that S(x) must satisfy in order for it to be a clamped. cubic spline interpolant for f(x) = sin"(x). Do not simplify the equations, just move all terms with unknown coefficients to the left of the equation and the known constants to the right. Also, do not evaluate the 's, leave them as in your equations. Set up the augmented matrix that needs to be solved to get the spline. DO NOT SOLVE THE SYSTEM DELIVERABLES: Show all your work ending with the 12 unsolved equations in the augmented matrix form