Math Help - Linear transformation

1. Linear transformation

Show that this is not a linear transformation

$T(\mathbf{x})=\begin{pmatrix}x_1^2\\x_2^2\end{pmat rix}$

Check scalar multiplication condition

$T(\lambda \mathbf{x})=\begin{pmatrix}\lambda ^2 x_1^2\\\lambda ^2 x_2^2\end{pmatrix}$

$=\lambda ^2\begin{pmatrix}x_1^2\\x_2^2\end{pmatrix}$

$\neq \lambda\begin{pmatrix}x_1^2\\x_2^2\end{pmatrix} \ \forall\lambda$

2. Just append $\lambda T(\mathbf{x})$ at the end there, and you'll have it.