sentences:  In this case, the row space is precisely the set of vectors ("x", "y", "z") ∈ "K"3 satisfying the equation "z" = 2"x" (using Cartesian coordinates, this set is a plane through the origin in three-dimensional space).For a matrix that represents a homogeneous system of linear equations, the row space consists of all linear equations that follow from those in the system.The column space of "A" is equal to the row space of "A"T.
  
  The row space is not affected by elementary row operations.