Question regarding nullity and basis of a kernel I was doing some exercises in a textbook and it required that I find the nullity of a linear transform. That I know how to do and you it by finding the kernel of that linear transform. It then asked to find a basis for that kernel of T. I was confused and noticed that the solution stated the same matrix that I used to find the nullity of T. My question is how is finding the nullity of T related to, or equivalent, to find a basis for the kernel of T?

The nullity is the dimension of the kernel and hence equal to however many vectors are in a basis for the kernel.
