For the general linear regression model, suppose we want to estimate l'B based on sample data, where l is a (k+1)x1 vector of constants. The Gauss Markov theorem tells us the most natural choices is also the best choice in a large class of possible estimators.

l'b is an unbiased estimator of l'B.

l'b = c0'y where c0'= l'(X'X)-1X' and c0 = X(X'X-1l)

Show for a general nX1 vector satisfying l = X'c, c'c is minimized when c=c0

continue from c'c = (c-c0+c0)'(c-c0+c0)