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evaluate: |(0,xy^(2),xz^(2)),(x^(2)y,0,y...

evaluate: `|(0,xy^(2),xz^(2)),(x^(2)y,0,yz^(2)),(x^(2)z,zy^(2),0)|`

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The correct Answer is:
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We have `|(0,xy^(2),xz^(2)),(x^(2)y,0,yz^(2)),(x^(2),zy^(2),0)|=x^(2)y^(2)z^(2)|(0,x,x),(y,0,y),(z,z,0)|`
[ taking `x^(2),y^(2)` and `z^(2)` common from `C_(1),C_(2)` and `C_(3)`, respectively]
`=x^(2)y^(2)z^(2)|(0,0,x),(y,-y,y),(z,z,0)| [ :. C_(2)toC_(2)-C-(3)]`
`=x^(2)y^(2)z^(2)[x(yz+yz)]`
`=x^(2)y^(2)z^(2).2xyz=2x^(3)y^(3)z^(3)`
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