Let foo, fio, foi, and fi1 be four coefficients at the corners of a uniform square and let f(x, y) be the function that performs a bilinear interpolation of these

coefficients. Bilinear interpolation can be expressed as the consecutive application of linear interpolation along each dimension. Show that the result of bilinear interpolation is independent of the order of linear interpolations, i.e., that linear interpolation can be performed in x-direction first followed by the y-direction or vice versa.