Answer :

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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