Answer
See answer below
Work Step by Step
We are given $A=\begin{bmatrix}
-3 & -6\\
-6 & -12
\end{bmatrix}$
We obtain rowspace $A=\begin{bmatrix}
-3 & -6\\
-6 & -12
\end{bmatrix} \approx \begin{bmatrix}
-3 & -6\\
0 & 0
\end{bmatrix}$
And colspace $A=\begin{bmatrix}
-3 & -6\\
-6 & -12
\end{bmatrix} \approx \begin{bmatrix}
-3 & 0\\
-6 & 0
\end{bmatrix}$
Thus the nullspace $(A)$ can be written as $Ax=0 \rightarrow \begin{bmatrix}
-3 & 0\\
-6 & 0
\end{bmatrix} \begin{bmatrix}
x\\
y
\end{bmatrix}= \begin{bmatrix}
0\\
0
\end{bmatrix} \\
\rightarrow y=-1 \\
\rightarrow x=-2y=-2(-1)=2$
Hence, the null space of the given matrix $A$ is $\{(2,-1)\}$
