Example 6. Find the polynomial  p[x]  that passes through the six points    using the following steps.
(a). Write down the linear system MC = B to be solved.
(b). Solve the linear system for the coefficients using our Gauss-Jordan subroutine.
(c). Construct the polynomial  p[x].

Solution 6.

(a). Write down the linear system MC = B to be solved.

Form the augmented matrix  M = [A,B].  

(b). Solve the linear system for the coefficients using our Gauss-Jordan subroutine.

This time use Mathematica to get the solution vector    out of this augmented matrix !

Or, we could use Mathematica's built in  LinearSolve[M,B]  procedure.

(c). Construct the polynomial  p[x].  The coefficients are stored in the array  c  and the elements are .

Of course we could do all this work in two lines by using Mathematica's built in  InterpolatingPolynomial[XY,x]  procedure.

We are done.

We can graph the polynomial, this is just for fun !

(c) John H. Mathews 2004