Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 300: 30

$(3,-2.5,-1)$

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. Hence $T(0,2,-1)=1.5T(1,1,1)-0.5T(0,-1,2)-1.5T(1,0,1)=1.5(2,0,-1)-0.5(-3,2,-1)-1.5(1,1,0)=(3,0,-1.5)+(1.5,-1,0.5)+(-1.5,-1.5,0)=(3,-2.5,-1)$