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.
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 – 1B
C11 = (– 1)1 + 1 (1 – 3) = – 2
C12 = (– 1)1 + 2 (4 – 3) = – 1
C13 = (– 1)1 + 3 (4 – 1) = 3
C21 = (– 1)2 + 1 (2 – 1) = – 1
C22 = (– 1)2 + 2 (3 – 1) = 2
C23 = (– 1)2 + 3 (3 – 2 ) = – 1
C31 = (– 1)3 + 1 (6 – 1) = 5
C32 = (– 1)3 + 2 (9 – 4) = – 5
C33 = (– 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.