Answer :

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 –

⇒ …(4)

Let,

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.

Adj(A) =

∴ 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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