nullity

$\operatorname{nullity}(A) = \dim\operatorname{Nul}(A)$ , the number of free variables.

The nullity of a matrix $A$ is the dimension of its null space, $\dim\operatorname{Nul}(A)$ — the number of free variables, and the number of independent directions you can move while staying a solution to $A\mathbf x=\mathbf 0$ . The rank-nullity theorem states $\operatorname{rank}(A)+\operatorname{nullity}(A)=n$ for any $m\times n$ matrix, since every column of RREF is either a pivot column or a free column, never both.