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 ^{– 1}B

C_{11 =} (– 1)^{1 + 1} (2 – 3) = – 1

C_{12} = (– 1)^{1 + 2} (5 – 3) = – 2

C_{13} = (– 1)^{1 + 3} (5 – 2) = 3

C_{21} = (– 1)^{2 + 1} (4 – 3) = – 1

C_{22} = (– 1)^{2 + 2} (2 – 3) = – 1

C_{23} = (– 1)^{2 + 3} (2 – 4 ) = – 2

C_{31} = (– 1)^{3 + 1} (12 – 6) = 6

C_{32} = (– 1)^{3 + 2} (6 – 15) = – 9

C_{33} = (– 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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