image.png
What's wrong
Your first vector has the wrong sign in the first entry—since x_1=2x_3-16x_4, the correct spanning set is
\left{\begin{bmatrix}2
-4
1
0\end{bmatrix},\begin{bmatrix}-16
8
0
1\end{bmatrix}\right}
, not
\left{\begin{bmatrix}-2
-4
1
0\end{bmatrix},\begin{bmatrix}-16
8
0
1\end{bmatrix}\right}
.
image.png
what bout this one
Nul A=\operatorname{span}\left{\begin{bmatrix}-3
1
0
0
0\end{bmatrix},\begin{bmatrix}2
0
-4
1
0\end{bmatrix}\right}
, so a spanning set is
\left{\begin{bmatrix}-3
1
0
0
0\end{bmatrix},\begin{bmatrix}2
0
-4
1
0\end{bmatrix}\right}
.
image.png
image.png
image.png
i can't read it
It says
Nul A=\operatorname{span}\left{\begin{bmatrix}-3
1
0
0
0\end{bmatrix},\begin{bmatrix}2
0
-4
1
0\end{bmatrix}\right}
, so the spanning set you should enter is
\left{\begin{bmatrix}-3
1
0
0
0\end{bmatrix},\begin{bmatrix}2
0
-4
1
0\end{bmatrix}\right}
.
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