Q. 295.0( 2 Votes )

The management co

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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