The demand and supply function of three related goods are given by
Qd1 = 120 - 4 P1 + 4 P3
Qs1 = -40 + 2 P1
Qd2 = 140 + 2 P1 - 2 P2 + 4 P3
Qs2 = -60 + 3P2
Qd3 = 150 - 3P1 + 2 P2 - 2 P3
Qs3 = -90 + 3P3
Write the system in a full 6 by 6 matrix form and find the equilibrium prices and quantities.