Answer
See below.
Work Step by Step
According to the Sum of Rank and Nullity Theorem: $Nullity(T)=dim(\rm I\!R)-rank(T)=3-3=0$.
$nullity(T)=dim(ker(T))$ by definition; thus the dimension of the kernel is $0$. Thus $ker(T)$ is $\{(0,0,0)\}$.
$rank(T)=dim(range(T))$ by definition; thus the dimension of the range is $3$. Thus $range(T)$ is $\rm I\!R^3$.
