Data interpolation has many applications. In this problem, we will answer: What is the degree 3 polynomial P(x) = ao + a + ax + 3x which passes through the points (-2, 6), (-1,4), (1,6), and (2,22). (a) (4 pts) Show that since P(-2) = 6, P(-1) = 4, P(1) = 6, and P(2) = 22, our problem is really the problem of solving the system of equations ao2a1 +4a2-8a3 = 6, ao a1 + a2 a3 = 4, ao + a + a2 + a3 = 6, ao + 2a1 +4a2 +8a3 = 22. (b) (4 pts) The system in part (a) is the matrix equation 1 -2 4 1 -1 1 1 1 1 1 2 4 -8 -1 1 8 -2 1 2 -1 Use A to solve the system of equations in (a). 1 The inverse of the above 4 x 4 matrix is 12 ao a1 a2 a3 8 8 -2 -8 8 -1 -2 -2 2 2 -2 1 6 4 6 22 (you don't have to show this).