Question

We know that null space of a mxn matrix with rank r is n-r. I think this wrong for some cases. Consider a square matrix that is invertible and suppose the unique solution it has got is zero vector. So, now the rank is same as n and hence n-r = 0. So the dimension of null space should be zero but its 1 with basis containing only null vector. Am I wrong somewhere?

Answer 1

lokeshh, the dimensionality of a space that contains only the zero vector is zero. Josh.

Answer 2

Thanks for the clarification. I didn't know that earlier!