As x members are awarded for honesty, y for helping others and z for supervising the workers.
According to question:
x + y + z = 12 …(1)
3(y + z) + 2x = 33 or 2x + 3y + 3z = 33 …(2)
And x + z = 2y or x – 2y + z = 0 …(3)
The above equations can be represented in matrix form as given below –
As A-1 =
∴ |A| =
Expanding about first row-
|A| = 1(3+6)-1(2-3)+1(-4-3) = 13-7 = 3
As |A| = 3 ≠ 0 , so solution is possible and unique.
Adj(A) can be determined by finding the co-factor matrix of A and taking its transpose.
∴ A-1 =
From equation 4 we have -
By matrix multiplication we get –
∴ 3 members are awarded for honesty, 4 for helping others and 5 for supervising the workers.
Apart from these, Society can include cleanliness for awarding the members.
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