Two institutions decided to award their employees for the three values of resourcefulness, competence and determination in the form of - Maths - Matrices

Question

Two institutions decided to award their employees for the three
values of resourcefulness, competence and determination in the form
of prices at the rate of Rs x, y and z respectively per person The
first institution decided to award respectively 4,3 and 2 employees
with a total price money of Rs 37000 and the second institution
decided to award respectively 5,3 and 4 employees with a total
price money of Rs 47000 If all the three prices per person together
amount to Rs 12000 then using matrix method find the value of x,y
and z

Rishabh Mittal · Accepted Answer

A T
Q4x+3y+2z=370005x+3y+4z=47000x+y+z=12000We can expressed these equations as AX=B
Where A=432534111,X=xyz  and B=370004700012000A=43-4-35-4+25-3=-4-3+4=-3≠0So, A is non singular therefore inverse 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=1Aadj A=-13-1-16-12-62-1-3X=A-1B=-13-1-16-12-62-1-3 370004700012000    =-13-37000-47000+72000-37000+94000-7200074000-47000-36000=-13-12000-15000-9000=400050003000So, x=4000 , y= 5000  and z=3000