Q. 365.0( 1 Vote )

# 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.*(CBSE 2014)*

*(CBSE 2014)*

Answer :

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 ^{– 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 = 100, y = 200 and z = 300

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