The row space of a matrix A is the vector subspace spanned by its linearly independent row vectors (that is, those that are not zero when in reduced row echelon form). Unlike the column space, the basis of the row space is not affected by elementary row operations. For example, the row space of the following matrix, which can be row-reduced to the second matrix, will be spanned by both and File:Linear subspaces with shading.svg This linear algebra-related article contains minimal information concerning its topic. You can help the Mathematics Wikia by adding to it.