For a linear transformation T: R^{n} → R^{m} given by an m by n matrix A, we have a special name for the kernel.
We remark that the null space of an m by n matrix is a subspace of R^{n}.
Example The subspace
{(x, y, z): x + y  z = 0, 2x  3y + z = 0} ⊂ R^{3}
given in an earlier example is in fact the null space of the matrix
[  1  1  1  ]. 
2  3  1 
Moreover, by



we have (1, 1, 1) ∉ nulA, and by



we have (2, 3, 5) ∈ nulA.