Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[NullSpace], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The procedure kernel computes a basis for the null space (kernel) of the linear transformation defined by the matrix A. The result is a set of vectors, possibly empty.

When given an optional second parameter, kernel(A, 'nulldim'), in addition to the above, assigns the variable nulldim the vector space dimension of the kernel (a non-negative integer).

The command with(linalg,kernel) allows the use of the abbreviated form of this command.

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

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

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

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

$\left\{\left[\begin{array}{ccc}\mathrm{-3}& 0& 1\end{array}\right]\right\}$