Answer
See below
Work Step by Step
A 5 × 7 matrix $A$ has $rank(A)+nullity (A)=7$
Since $A$ has $5$ rows, $rank (A) \leq 5 \\
\rightarrow nullity (A) \geq 2$
Since nullity (A) is a subspace of $R^7$, then $nullity (A) \leq 7$
An example of a $5 × 7$ matrix $A$ with $nullity(A) = 2$
$\begin{bmatrix}
1 & 0 &0 & 0 & 0& 0 & 0\\
0 & 1 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 1 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 1 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 1 & 0 & 0\\
\end{bmatrix}$
A $5 × 7$ matrix A with $nullity(A) = 7$ is $0_{5\times 7}$
