Answer
See below
Work Step by Step
Given: $A=\begin{bmatrix}
2 & -4\\1 & 2\\-3 & 5
\end{bmatrix}$
Obtain: $\begin{bmatrix}
2 & -4\\1 & 2\\-3 & 5
\end{bmatrix}\begin{bmatrix}
x_1\\x_2
\end{bmatrix}=0$
We have the system:
$2x_1-4x_2=0\\
x_1+2x_2=0\\
-3x_1+5x_2=0\\
\rightarrow x_1=x_2=0$
Then $N(A)=(x_1,x_2) \in R^2:x_1=x_2=0)$
Hence, $N(A)=span (0,0)$