A crucial step in the proof of the Gauss-Markov theorem (Section XXXXXXXXXXuses the fact that the matrix product AX must be 0 because AX = 0. Why is this the case? [Hint: The key here is that AXβ = 0...

A crucial step in the proof of the Gauss-Markov theorem (Section 9.3.2) uses the fact that the matrix product AX must be 0 because AX = 0. Why is this the case? [Hint: The key here is that AXβ = 0 regardless of the value of fl. Consider, for example, fl ¼ =1; 0; ... ; 0% 0 (i.e., one possible value of fl). Show that this implies that the first row of AX is 0. Then consider fl = 0; 1; ... ; 0% 0 , and so on.]