I'm asked to show that transformation $ T(a_1, a_2) = (a_1, a_1^2)$ is not linear.
My attempt at was by showing that it is not closed under addition. That is; $T[(a_1, a_2)+(b_1,b_2)] \ne T(a_1, a_2)+T(b_1, b_2)$
and I got $ \begin{matrix}a_1+b_1 \\a_1^2+b_1^2 \end{matrix} \ \ \ne \ \ \begin{matrix}a_1+b_1 \\a_1^2 + 2a_1b_1+b_1^2 \end{matrix} $
Is this a good way to show it's not linear? Is it valid?