निम्नलिखित समीकरणों को क्रेमर के नियम से हल कीजिएः
x+y+z=9
2x+5y+7z=52,
2x+y-z=0.

Explanation

`Delta=|(1,1,1),(2,5,7),(2,1,-1)|`
`=1(-5-7)+1(14+2)+1(2-10)`
`=-12+16-8=-4`
`Delta_(1)=|(9,1,1),(52,5,7),(0,1,-1)|`
`=9(-5-7)+1(0+52)+1(52-0)`
`=-108+52+52=-4`
`Delta_(2)=|(1,9,1),(2,52,7),(2,0,-1)|`
`=1(-52-0)+9(14+2)+1(0-104)`
`=-52+144-104=-12`
`Delta_(3)=|(1,1,9),(2,5,52),(2,1,0)|`
`=1(0-52)-1(104-0)+9(2-10)`
`=-52+104-72=-20`
क्रैमर विधि से,
`x=(Delta_(1))/(Delta)=(-4)/(-4)=1`
`y=(Delta_(2))/(Delta)=(-12)/(-4)=3`
`z=(Delta_(3))/(Delta)=(-20)/(-4)=5`
`thereforex=1,y=3,z=5`