Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctuality. The school P wants to award ₹x each, ₹y each and ₹z each for the three respectively values to its 3, 2 and 1 students with a total award money of ₹1,000. School Q wants to spend ₹1,500 to award its 4,1 and 3 students on the respective values (by giving the same award money for three values as before.) If the total amount of awards for one prize on each value is ₹600, using matrices, find the award money for each value, Apart on each value is ₹600, using matrices, find the award money for each value, Apart from the above three values, suggest one more value for awards.
x,y and z be the prize amount per student for Discipline, Politeness and Punctuality respectively.
3x + 2y + z = 1000
4x + y + 3z = 1500
x + y + z = 600
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 = 100, y = 200 and z = 300