Chapter 6 - Linear Transformations - 6.5 Applications of Linear Transformations - 6.5 Exercises - Page 335: 6

a) $(x,x+y)$ b) This is a vertical expansion (with a factor of $2$) of the point.

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. a) Hence here $T(x,y)=xT(1,0)+yT(0,1)=x(1,1)+y(0,1)=(x,x)+(0,y)=(x,x+y)$ b) This is a vertical expansion (with a factor of $2$) of the point.