Q. 355.0( 3 Votes )

# Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award ₹x each ₹y each and ₹ z each for the three respective values to 3, 2 and 1 students respectively with total award money of ₹16,00. School B wants to Spend ₹2,300 to award its 4,1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is ₹900, using matrices, find the award money for each value, Apart from these three values, suggest one more value which should be considered for the award.

Answer :

Let the numbers are x, y,z be the prize amount per person for sincerity, truthfulness and helpfulness respectively

As per the given data we get,

3x + 2y + z = 1600

4x + y + 3z = 2300

x + y + z = 900

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 = 200, y = 300 and z = 400

Excellence in extra curricular activities should be another value considered for an award.

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