Answer
$nullity (A)=1$
Work Step by Step
We are given $A=\begin{bmatrix}
0 &1 & 0\\
0 & 1 & 0\\
0 & 0 & 1\\
0 & 0 & 1
\end{bmatrix}$
In this problem, A is a $3 \times 4$ matrix, and so, in the Rank-Nullity Theorem, $n = 3$. Further, from the foregoing row-echelon form of the augmented matrix of the system
Ax = 0, we see that $rank(A) = 2$.
Hence:
$$rank (A)+nullity(A)=n \\
nullity (A)=n-rank (A)=3-2=1$$
