UPSC NDA Math Model Paper 1

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x	y	z
a	b	c
x+a	y+b	z+c

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Apply R1→R1+R2
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x+a	y+b	z+c
a	b	c
x+a	y+b	z+c

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As we can see that the first and the third row of the given matrix are equal.
We know that, if any two rows (columns) of a matrix are same then the value of the determinant is zero.
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x	y	z
a	b	c
x+a	y+b	z+c

|=0