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

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

The function rank computes the rank of a matrix, by performing Gaussian elimination on the rows of the given matrix. The rank of the matrix A is the number of non-zero rows in the resulting matrix.

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

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

$A≔\mathrm{matrix}\left(3\,3\,\left[x\,1\,0\,0\,0\,1\,xy\,y\,1\right]\right)$

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

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

$2$