two institutions decided to award their employees in the form of prizes at the rate of Rs x, Rs y, Rs z respectively per person. the first institution decides to award respectively 4, 3 and 2 employees with total prize money of Rs 37,000 and second institution decides to award respectively 5, 3 and 4 employees with the total prize money of Rs 47,000. if all the three prizes per person together amount to Rs 12,000 then using matrix method find the value of x, y and z.

Dear Student,
Please find below the solution to the asked query:

Given, 4x+3y+2z=370005x+3y+4z=47000x+y+z=12000we can express these equations in matrix form as AX=Bwhere A=432534111, X=xyz and B=370004700012000A = 432534111A=43-4-35-4+25-3A=-3   0hence A is non singular and A-1 exists.A11=-1     A12=-1    A13=2A21=-1     A22=2        A23=-1A31=6        A32=-6     A33=-3adj A=-1-16-12-62-1-3A-1=1AadjA=-13-1-16-12-62-1-3X=A-1B=-13-1-16-12-62-1-3370004700012000xyz=-13-37000-47000+72000-37000+94000-7200074000-47000-36000=400050003000By the definition of equality of matrices, so x=4000, y=5000, z=3000

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