Q. 165.0( 3 Votes )

# Two factories dec

Answer :

Let the numbers are x, y,z be the prize amount per person for adaptability, carefulness and calmness respectively

As per the given data we get,

2x + 4y + 3z = 29000

5x + 2y + 3z = 30500

X + y + z = 9500

These three equations can be written as A X = B

|A| = 2(2 – 3) – 4(5 – 3) + 3(5 – 2)

= 2(– 1) – 4(2) + 3(3)

= – 2 – 8 + 9

= – 1

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

C11 = (– 1)1 + 1 (2 – 3) = – 1

C12 = (– 1)1 + 2 (5 – 3) = – 2

C13 = (– 1)1 + 3 (5 – 2) = 3

C21 = (– 1)2 + 1 (4 – 3) = – 1

C22 = (– 1)2 + 2 (2 – 3) = – 1

C23 = (– 1)2 + 3 (2 – 4 ) = – 2

C31 = (– 1)3 + 1 (12 – 6) = 6

C32 = (– 1)3 + 2 (6 – 15) = – 9

C33 = (– 1)3 + 3 (4 – 20) = – 16

Adj A = X = A – 1 B = X = X = X =  = Hence, x = 2500, y = 3000 and z = 4000

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