Solution D.C36 Chris Black

The row reduced form of matrix $A$ is $\begin{bmatrix} \leading{1} & 0 & -1 & 3 & 5\\ 0 & \leading{1} & 1& -1 & 3\\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}$, so the rank of $A$ (the number of pivot columns) is $2$, and the nullity is $5 - 2 = 3$.