Use theorem $4\mathrm{.}3\mathrm{.}2($Transformation is linear transformation if and only if $1)T(u+v)=T(u)+T(v)$ and $2)T(cu)=cT(u)$ to determine whether $T$:$R^2$ maps to $R^2$ is a linear transformation $T(x,y)=(x^2,y)$