Affine solution space
= Affine solution space
{title2=$\{x:Ax=b\}=x_0+\ker A$}
If a <linear system> $Ax=b$ has one solution $x_0$, every other solution differs from it by an element of the <null space>: $Ax=b$ is equivalent to $A(x-x_0)=0$. Its solution set is therefore the displayed <affine subspace>, of dimension equal to the <nullity>. If the system is inconsistent, the solution set is empty, rather than a translate of the kernel.