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 respective 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 the 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 from the above three values, suggest one more value for awards.
We have,
3x+2y+z=1000
4x+7+3z=1500
x+y+z=600
The given system of equations can be written as AX = B ,
Where 
Now, |A| = 
= 3(1-3)-2(4-3)+1(4-1)
=-6-2+3 = -8+3 = -5 ≠ 0
So the given system of equation has a unique solution given by
X =A-1B
Co-factors are ,
Similarly we can find all co-factors
C11 = -2 , C12 = -1, C13 = 3
C21 = -1 , C22 = 2, C23 = -1
C31 = 5 , C32 = -5, C33 = -5
∴
Now, X =A-1B
∴ x = 100, y=200 and z=300
i.e Rs. 100 forDiscipline, Rs. 200 for Politeness and Rs. 300 for Punctuality.
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