Answer
See below
Work Step by Step
Given: $A=\begin{bmatrix}
1 & -3 & 2
\end{bmatrix}$
Obtain: $\begin{bmatrix}
1 & -3 & 2
\end{bmatrix}\begin{bmatrix}
x_1\\x_2\\x_3
\end{bmatrix}=0$
We have the system:
$x_1-3x_2+2x_3=0\\
\rightarrow x_1=3x_2-2x_3$
Then $N(A)=(x_1,x_2,x_3) \in R^3:x_1=0)\\
\rightarrow (x_1,x_2) \in N(A),x_1=3x_2-2x_3\\
\rightarrow (3x_2-2x_3,x_2,x_3)=x_2(3,1,0)+x_3(-2,0,1)$
Hence, $N(A)=span ((3,1,0),(-2,0,1))$
