Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 300: 12

Not linear.

In this case the transformation is linear if $T(v_1+v_2)=T(v_1)+T(v_2)$ and $T(av_1)=aT(v_1)$ for any $v_1,v_2$ in the domain and any $a$ scalar. Here this is violated because e.g. $T(1,1,1)=(2,2,2)$, $T(0,0,0)=(1,1,1)$ but $T((1,1,1)+(0,0,0))=T(1,1,1)=(2,2,2)\ne(3,3,3)=(2,2,2)+(1,1,1)=T(1,1,1)+T(0,0,0).$