Q. 195.0( 2 Votes )

# Two schools P and

Answer :

x, y and z be the prize amount per student for Discipline, Politeness and Punctuality respectively.

3x + 2y + z = 2200

4x + y + 3z = 3100

x + y + z = 1200

These three equations can be written as

A X = B

|A| = 3(1 – 3) – 2(4 – 3) + 1(4 – 1)

= 3(– 2) – 2(1) + 1(3)

= – 6 – 2 + 3

= – 5

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

C_{11 =} (– 1)^{1 + 1} (1 – 3) = – 2

C_{12} = (– 1)^{1 + 2} (4 – 3) = – 1

C_{13} = (– 1)^{1 + 3} (4 – 1) = 3

C_{21} = (– 1)^{2 + 1} (2 – 1) = – 1

C_{22} = (– 1)^{2 + 2} (3 – 1) = 2

C_{23} = (– 1)^{2 + 3} (3 – 2 ) = – 1

C_{31} = (– 1)^{3 + 1} (6 – 1) = 5

C_{32} = (– 1)^{3 + 2} (9 – 4) = – 5

C_{33} = (– 1)^{3 + 3} (3 – 8) = – 5

Adj A =

X = A ^{– 1} B =

X =

X =

X =

=

Hence, x = 300, y = 400 and z = 500

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