Answer
See below
Work Step by Step
Given $A=\begin{bmatrix}
1 & 3 &-2 & 1\\ 3 & 10 & -4 & 6 \\ 2 & 5 & -6 &-1
\end{bmatrix}$
Since $x,y,z,w \in nullspace (A)$ we obtain
$Ax=0\\\begin{bmatrix}
1 & 3 &-2 & 1\\ 3 & 10 & -4 & 6 \\ 2 & 5 & -6 &-1
\end{bmatrix}\begin{bmatrix}
x \\ y \\ z \\ w
\end{bmatrix}=0\\
\begin{bmatrix}
x +3y -2z +w\\ 3x+10y -4z+ 6w \\ 2x+ 5y -6z-1w
\end{bmatrix}=0\\
\rightarrow x +3y -2z +w=0\\
3x+10y -4z+ 6w =0\\
2x+ 5y -6z-1w =0\\
\rightarrow 3x+10y-4z+6w-(x +3y -2z +w)=y+2z+3w=0 \rightarrow y=-2z-3w\\
\rightarrow x +3y -2z +w-3(y+2z+3w)=x-8z-8w=0 \rightarrow x=8z+8w$
Then $x=(8z+8w,-2z-3w,z,w)=(8z,-2z,z,0)+(8w,-3w,0,w)=z(8,-2,1,0)+w(8,-3,0,1)$
Hence, nullspace $(A) \subset \{z(8,-2,1,0)+w(8,-3,0,1):z,w \in R\}$
