complementary slackness of linear programming- note knowledge of theorem #7 is not necessary because the desired method is using matrix algebra only

Consider the normalform primal LP min 11) = ch (Objective Function) Primal: s.t. Ax 2 b (Constraints #1 through #m) x 2 0 (Sign Restrictions #1 though #10) and its normalform dual max 2 : pr (Objective Function) s.t. ATp g c (Constraints #1 through #n) p Z 0 (Sign Restrictions #1 though #m) which, when placed in standard forms become min 2:) = ch (Objective Function) Ax Ie : b (Constraints #1 through #m) x, e Z 0 (Sign Restrictions #1 though #71) max 2 = pr (Objective Function) ATp + Is = c (Constraints #1 through #n) p, s 2 0 (Sign Restrictions #1 though #m) The purpose of this problem is for you to prove Complementary Slack ness using a different approach than that taken in the notes and in class, and so using the above standard forms and without using the results of Theorem #7, prove that at optimal solutions for both the primal and the dual, we must have mas, = 0 for all i = 1,2, 3,...,n and pie,- = 0 for all j = 1, 2,3, ..., m. Him: This should only take a little bit of matrix algebra