Correcting Vector Sign Error

Your first vector has the wrong sign in the first entry—since $x_1=2x_3-16x_4$, the correct spanning set is

$$\left\{\left[\begin{array}{c}2\text{-}4\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}-16\\ 8\\ 0\\ 1\end{array}\right]\right\}$$

, not

$$\left\{\left[\begin{array}{c}-2\text{-}4\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}-16\\ 8\\ 0\\ 1\end{array}\right]\right\}$$

.

$$\text{Nul }A=\mathrm{span}\left\{\left[\begin{array}{c}-3\\ 1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}2\\ 0\text{-}4\\ 1\\ 0\end{array}\right]\right\}$$

, so a spanning set is

$$\left\{\left[\begin{array}{c}-3\\ 1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}2\\ 0\text{-}4\\ 1\\ 0\end{array}\right]\right\}$$

.

It says

$$\text{Nul }A=\mathrm{span}\left\{\left[\begin{array}{c}-3\\ 1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}2\\ 0\text{-}4\\ 1\\ 0\end{array}\right]\right\}$$

, so the spanning set you should enter is

$$\left\{\left[\begin{array}{c}-3\\ 1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}2\\ 0\text{-}4\\ 1\\ 0\end{array}\right]\right\}$$

.