A salesman has the following record of sales during three months for three items `A, B and C` which have different rates of commission Month, Sale of units, Total commissiondrawn (in Rs) Find out the rates of commission on items `A, B and C` by using deter-minant method.

Explanation

Consider x,y,z be the rates of commission on items A,B,C
Then we get the systems of linear equations as `90x+100y+20z=800`,

`130x+50y+40z=900`,

`60x+100y+30z=850`

`9x+10y+2z=80`,
`13x+5y+4z=90`,
`6x+10y+3z=85`

As we know that the system of linear equation can be written in matrix form as `AX = B`

`implies A=|(9,10,2),(13,5,4),(6,10,3)|`,`X=[(x),(y),(z)]`,`B=[(80),(90),(85)]`

Now find the determinant of `A`,

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