Answer
Nul A= Span $\{ \left[\begin{array}{l}
2\\
1\\
0\\
0\\
0
\end{array}\right],\ \left[\begin{array}{l}
-4\\
0\\
9\\
1\\
0
\end{array}\right] \}$
Work Step by Step
By definition,
Nul A =$\{$x$: $ x$\in \mathbb{R}^{n}$ and Ax=0 $\}$.
---------
We find the general solution to Ax=0:
$[$A $0]$ = $\left[\begin{array}{llllll}
1 & -2 & 0 & 4 & 0 & 0\\
0 & 0 & 1 & -9 & 0 & 0\\
0 & 0 & 0 & 0 & 1 & 0
\end{array}\right]$
With $x_{2}$ and $x_{4}$ free parameters (any real numbers),
$x_{1}=2x_{2}-4x_{3}$
$x_{3}=9x_{4}$
$x_{5}=0$
$x=\left[\begin{array}{l}
2x_{2}-4x_{4}\\
x_{2}\\
9x_{4}\\
x_{4}\\
0
\end{array}\right]=x_{2}\left[\begin{array}{l}
2\\
1\\
0\\
0\\
0
\end{array}\right]+x_{4}\left[\begin{array}{l}
-4\\
0\\
9\\
1\\
0
\end{array}\right]$
Nul A= Span $\{ \left[\begin{array}{l}
2\\
1\\
0\\
0\\
0
\end{array}\right],\ \left[\begin{array}{l}
-4\\
0\\
9\\
1\\
0
\end{array}\right] \}$
