Associated matrix with respect to given bases

Let $f : R^{2} \to R^{3}$ , $f (x, y) = (x, y, x + y)$ . Find $M_{C}^{B} (f)$ with

B = ((1, 1), (1, - 1)), C = ((1, 0, 0), (1, 1, 0), (1, 1, 1)) .

The full solution of this exercise is in the unlocked version.