# Two schools P and

x, y and z be the prize amount per student for Discipline, Politeness and Punctuality respectively.

3x + 2y + z = 2200

4x + y + 3z = 3100

x + y + z = 1200

These three equations can be written as A X = B

|A| = 3(1 – 3) – 2(4 – 3) + 1(4 – 1)

= 3(– 2) – 2(1) + 1(3)

= – 6 – 2 + 3

= – 5

Hence, the unique solution given by x = A – 1B

C11 = (– 1)1 + 1 (1 – 3) = – 2

C12 = (– 1)1 + 2 (4 – 3) = – 1

C13 = (– 1)1 + 3 (4 – 1) = 3

C21 = (– 1)2 + 1 (2 – 1) = – 1

C22 = (– 1)2 + 2 (3 – 1) = 2

C23 = (– 1)2 + 3 (3 – 2 ) = – 1

C31 = (– 1)3 + 1 (6 – 1) = 5

C32 = (– 1)3 + 2 (9 – 4) = – 5

C33 = (– 1)3 + 3 (3 – 8) = – 5

Adj A = X = A – 1 B = X = X = X =  = Hence, x = 300, y = 400 and z = 500

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