Solution D.C35 Chris Black

The row reduced form of matrix $A$ is $\begin{bmatrix} \leading{1} & 0 & 0\\ 0 & \leading{1} & 0\\ 0 & 0 & \leading{1}\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{bmatrix}$, so the rank of $A$ (number of pivot columns) is $3$, and the nullity is $0$.