Answer
See below.
Work Step by Step
According to the Sum of Rank and Nullity Theorem: $Nullity(T)=dim(\rm I\!R)-rank(T)=3-2=1$.
$nullity(T)=dim(ker(T))$ by definition; thus the dimension of the kernel is $1$. Thus $ker(T)$ is a line.
$rank(T)=dim(range(T))$ by definition; thus the dimension of the range is $2$. Thus $range(T)$ is a plane.
