Answer
See below
Work Step by Step
Given: $A=\begin{bmatrix}
1 & -2 & 1\\4 & - 7 & -2\\ -1 & 3 & 4
\end{bmatrix}$
Obtain: $\begin{bmatrix}
1 & -2 & 1\\4 & - 7 & -2\\ -1 & 3 & 4
\end{bmatrix}\begin{bmatrix}
x_1\\x_2\\x_3
\end{bmatrix}=0$
We have the system:
$x−2x_2+x_3=0\\4x_1−7x_2−2x_3=0\\−x_1+3x_2+4x_3=0$
From exercise 27, we have $x_1=x_2=x_3=0$
Then $N(A)=(0,0,0)$
Hence, $N(A)=span (0,0,0)$
