Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 300: 9

Not a linear transformation.

The function $T(x,y)=(x,1)$ is not a linear transformation. This is because, one can see that $$T((x_1,y_1)+(x_2,y_2))=T(x_1+x_2,y_1+y_2)=(x_1+x_2,1)$$ and $$T(x_1,y_1)+T(x_2,y_2)=(x_1,1)+(x_2,1)=(x_1+x_2,2).$$ Hence $$T((x_1,y_1)+(x_2,y_2))\neq T(x_1,y_1)+T(x_2,y_2).$$