The procedure null(A) computes a basis for the null space (kernel) of the linear transformation defined by the matrix A. The result is a matrix where each column represents a vector in the computed basis.

The basis vectors are not in any fixed order.  The same input in the same session can result in a matrix with columns in a different order than the previous execution.

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,1\right]\,\left[2\,4\,2\right]\,\left[2\,8\,1\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 1\\ 2& 4& 2\\ 2& 8& 1\end{array}\right]$

$\mathrm{null}\left(A\right)$

$\left[\begin{array}{c}-\frac{3}{2}\\ \frac{1}{4}\\ 1\end{array}\right]$