# Math Help - null,dimension exam approaching!!

1. ## null,dimension exam approaching!!

Hi!
Suppose that A and B are mxn matrices
(i)Using dimension thm(or otherwise)show that Null(A)=R^n if and only if A=0
ii)Using (i)(or otherwise)prove that A=B if and only if Ax=Bx for all x is an element of R^n

Thanks.

2. ## Re: null,dimension exam approaching!!

I am not sure about the dimension theorem, but if a matrix has a non-zero element, it is easy to write a vector that, when multiplied by the matrix, gives a non-zero vector. Point ii) follows immediately from i).