The RowSpace(A) (ColumnSpace(A)) command returns a list of row (column) Vectors that form a basis for the Vector space spanned by the rows (columns) of Matrix A.  The Vectors are returned in canonical form with leading entries 1.

The row space (column space) of a zero Matrix is the empty list.

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

$A≔⟨⟨1\,2\,0⟩\left|⟨0\,2\,6⟩\right|⟨0\,1\,3⟩|⟨1\,1\,-3⟩⟩$

$A≔\left[\begin{array}{cccc}1& 0& 0& 1\\ 2& 2& 1& 1\\ 0& 6& 3& \mathrm{-3}\end{array}\right]$

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

$\left[\left[\begin{array}{cccc}1& 0& 0& 1\end{array}\right]\,\left[\begin{array}{cccc}0& 1& \frac{1}{2}& -\frac{1}{2}\end{array}\right]\right]$

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

$\left[\left[\begin{array}{c}1\\ 0\\ \mathrm{-6}\end{array}\right]\,\left[\begin{array}{c}0\\ 1\\ 3\end{array}\right]\right]$