on one hand, r + Ax = b and A*r = 0, that is, A*b-A*Ax=0 or
A*Ax-A*b=0.
on the other hand,we have
the square of = (Ax-b)*(Ax-b)=(x*A*-b*)(Ax-b)=x*A*Ax-2b*Ax+b*b
taking the derivative, x minimizes if and only if
2A*Ax-2A*b=0 that is A*Ax-A*b=0.
I am supposed to work out to show that it has a solution where x minimizes . I guess my question is where to even begin. When I do the block matrix multiplication, I get:
Which tells me r + Ax = b and A*r = 0... but I don't know how to complete it or bring in the minimization?