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|(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0)| is...

`|(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0)|` is equal to……………

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The correct Answer is:
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We have `|(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0)|=|(z-x,xyz,x-z),(z-x,0,y-z),(z-x,z-y,0)| [ :' C_(1)toC_(1)-C_(3)]`
`=(z-x)|(1,xyz,x-z),(1,0,y-z),(1,z-y,0)|`
[taking `(z-x)` common from column 1]
Expanding along `R_(1)`
`=(z-x)[1.{-(y-z)(z-y)}-xyz(z-y)+(x-z)(z-y)]`
`=(z-x)(z-y)(-y+z-xyz+x-z)`
`=(z-x)(z-y)(x-y-xyz)`
`=(z-x)(y-z)(y-x+xyz)`
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