The solution space of a system of equations is its solution set, regarded together with any algebraic structure inherited from the ambient space. For a homogeneous linear system
 |
the solution space is the null space of 
and is a vector subspace. If
the inhomogeneous linear system 
is consistent and 
is one solution, every solution has the form
 |
where 
.
Its solution space is therefore an affine space parallel
to the null space.
