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.