I'm studying for a test, and I need help with this problem. I am not sure how to prove that this is not linear due to the notation. The comma is throwing me off.
Show that the transformation $T$ defined by $T(x_1,x_2)$ = $(x_1^2-2x_2, x_1+5x_2)$ is not linear.
I know that the definition of a linear transformation involves:
$T(u+v)=T(u)+T(v)$ for all $u, v$ in the domain of $T$.
$T(c*u) = c*T(u)$ for all scalars $c$ and all $u$ in the domain of $T$.
$T(cu + dv) = cT(u) + dT(v)$ for all vectors $u, v$ in the domain of $T$ and all scalars $c, d$
$T(0) = 0$ if $T$ is linear
However, I'm not sure how to use this definition with the specific function given.
Would $T(x_1 + x_2)$ = $T(x_1) + T(x_2)$ work?