Editing Linear subspace (section)

===Basis for a row space===
:'''Input''' An ''m''&nbsp;×&nbsp;''n'' matrix ''A''.
:'''Output''' A basis for the row space of ''A''.
:# Use elementary row operations to put ''A'' into row echelon form.
:# The nonzero rows of the echelon form are a basis for the row space of ''A''.
See the article on [[row space]] for an [[Row and column spaces#Basis 2|example]].

If we instead put the matrix ''A'' into reduced row echelon form, then the resulting basis for the row space is uniquely determined. This provides an algorithm for checking whether two row spaces are equal and, by extension, whether two subspaces of ''K''<sup>''n''</sup> are equal.