Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 302: 70

a)$(y,x)$ b) The point being reflected to the line $y=x$.

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 $T(x,y)=xT(1,0)+yT(0,1)=x(0,1)+y(1,0)=(0,x)+(y,0)=(y,x)$ b) This is the point being reflected to the line $y=x$.