Given a matrix the nullspace is the set of all so that where is zero vector in . To find the nullspace you basically need to solve the homogenous equation . If you convert this problem in Gaussian-Jordan elimination, it means you need to solve the equation where was an attached coloumn of zeros (corresponding to the fact that we are solving a homogenous system). Therefore, you end up with (notice the new coloum of zeros):
This matrix is telling us that (the last two coloums do not tell us anything):
Thus,
.
If we let then:
Are always in the nullspace.
Thus, the nullspace is,
Can you find a basis now?