Consider the determinant ∆=|\table a_{11} , a_{12} , a_{13} ; a_{21} , a_{22} , a_{23} ; a_{31} , a_{32} , a_{33} | . If a_{13}=y z, a_{23}=z x, a_{33}=x y and the minors of a_{13}, a_{23}, a_{33} are respectively (z-y),(z-x),(y-x) then what is the value of ∆ ? [NDA II 2022]

Correct Answer is : (z−y)(z−x)(y−x)

UPSC NDA 2 2022 Mathematics Solved Paper

Question : 5 of 120

Marks: +1, -0

Consider the determinant
∆=|

|.
If a13=yz,a23=zx,a33=xy and the minors of a13,a23,a33 are respectively (z−y),(z−x),(y−x) then what is the value of ∆ ?

[NDA II 2022]

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