using linear algebra calculate the equilibrium P_{1},P_{2},P_{3} for the following three good market model.
(1) Qs1=-7+P1
(2) Qd1=15-P1+2P2+P3
(3) Qs1=Qd1
(4) Qs2=-4+4P2
(5) Qd2=9+P1-P2-P3
(6) Qs2=Qd2
(7) Qs3=-5+2P3
(8) Qd3= 8+2P1-P2-4P3
(9) Qs3=Qd3