Answer
See below
Work Step by Step
Given: $A=\begin{bmatrix}
1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8
\end{bmatrix}$
Obtain $A=\begin{bmatrix}
1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8
\end{bmatrix}\begin{bmatrix}
x_1\\x_2\\x_3\\x_4
\end{bmatrix}$
From exercise 26, we have: $x_1=x_3+x_4\\x_2=-2x_3-3x_4\\
\rightarrow (x_1,x_2,x_3,x_4)\\=(x_3+x_4,-2x_3-3x_4,x_3,x_4)\\ =x_3(1,-2,1,0)+x_4(1,-3,0,1)$
then $N(A)=(1,-2,1,0),(1,-3,0,1)$
Hence, $N(A)=span (1,-2,1,0),(1,-3,0,1)$
