NullSpace(A) returns a basis for the linear system A x = 0 over the field F as a set of Vectors B = {b1, b2, ...}.

The (indexed) parameter F, which specifies the domain of computation, a field, must be a Maple table/module which has the following values/exports:

F[`0`]: a constant for the zero of the ring F

F[`1`]: a constant for the (multiplicative) identity of F

F[`+`]: a procedure for adding elements of F (nary)

F[`-`]: a procedure for negating and subtracting elements of F (unary and binary)

F[`*`]: a procedure for multiplying two elements of F (commutative)

F[`/`]: a procedure for dividing two elements of F

F[`=`]: a boolean procedure for testing if two elements in F are equal

$\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Generic}\right]\right)\:$

$Q\left[\mathrm{`0`}\right],Q\left[\mathrm{`1`}\right],Q\left[\mathrm{`+`}\right],Q\left[\mathrm{`-`}\right],Q\left[\mathrm{`*`}\right],Q\left[\mathrm{`/`}\right],Q\left[\mathrm{`=`}\right]≔0,1,\mathrm{`+`},\mathrm{`-`},\mathrm{`*`},\mathrm{`/`},\mathrm{`=`}$

$Q_0,Q_1,Q_{\mathrm{`+`}},Q_{\mathrm{`-`}},Q_{\mathrm{`*`}},Q_{\mathrm{`/`}},Q_{\mathrm{`=`}}≔0,1,\mathrm{`+`},\mathrm{`-`},\mathrm{`*`},\mathrm{`/`},\mathrm{`=`}$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,3\right]\,\left[1\,3\,5\right]\,\left[0\,1\,2\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 3\\ 1& 3& 5\\ 0& 1& 2\end{array}\right]$

$\mathrm{NullSpace}\left[Q\right]\left(A\right)$

$\left\{\left[\begin{array}{c}1\\ \mathrm{-2}\\ 1\end{array}\right]\right\}$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,3\right]\,\left[2\,4\,6\right]\,\left[-1\,-2\,-3\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ \mathrm{-1}& \mathrm{-2}& \mathrm{-3}\end{array}\right]$

$\mathrm{NullSpace}\left[Q\right]\left(A\right)$

$\left\{\left[\begin{array}{c}\mathrm{-2}\\ 1\\ 0\end{array}\right]\,\left[\begin{array}{c}\mathrm{-3}\\ 0\\ 1\end{array}\right]\right\}$