We know that to prove a transformation is linear we need to show that
$$T(x_1, y_1)+T(x_2, y_2)=T(x_1+x_2, y_1+y_2)$$
$$ kT(x,y) = T(kx, ky)$$
But I can’t think of a transformation which satisfies the first condition but not the second one? Does anyone know one example of this??