Given that xl is a solution of the normal equations, A^(t)Ax=A^(t)b.

Suppose that Az is inside of range(A) for z an nx1 and that

(b-Az)^(t)(b-Az) <= (b-Axl)^(t)(b-Axl).

I need to show that Az = Axl.

I'm thinking a proof by contradiction, assuming that the inequality is not true, but can't seem to get too far along. Thanks for any help.