Find the plane that gives the best fit to the 4 values b = (0, 1, 3, 4) at the corners (1, 0) and (0, 1) and (-1, 0) and (0, -1) of a square. The equations C + Dx+ Ey = b at those 4 points are Ax = b with 3 unknowns x = ( C, D, E). What is A? At the center (0, 0) of the square, show that C + Dx + Ey = average of the b's.

Find the plane that gives the best fit to the 4 values b = (0, 1, 3, 4) at the corners (1, 0) and (0, 1) and (-1, 0) and (0, -1) of a square. The equations C + Dx+ Ey = b at those 4 points are Ax = b with 3 unknowns x = ( C, D, E). What is A? At the center (0, 0) of the square, show that C + Dx + Ey = average of the b's.