Two schools P and

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.