Be $F(x, y) = 3x + 4y$. I have to prove it's a linear appliction.
I am confused about the way to proceed. Is this the right way to proceed?
$$F(x_1 + x_2, y_1 + y_2) = 3(x_1 + x_2) + 4(y_1 + y_2) = 3x_1 + 4y_1 + 3x_2 + 4y_2 = F(x_1, y_1) + F(x_2, y_2)$$
Sorry for this silly question, I just have to acquire more confidence I guess...