UPSC NDA Math Model Paper 10

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x−y	y−z	z−x
y−z	z−x	x−y
z−x	x−y	y−z

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Apply R1→R1+R2+R3, We get
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0	0	0
y−z	z−x	x−y
z−x	x−y	y−z

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As we can see that the entry of the first row is zero.
We know that,
If each entry in any row or column of a determinant is 0, then the value of the determinant is zero.
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x−y	y−z	z−x
y−z	z−x	x−y
z−x	x−y	y−z

|=0