Consider the determinant
∆=| able 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]

Question

Consider the determinant
∆=|	able 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]

Examsnet · Accepted Answer

Correct Answer is : (z−y)(z−x)(y−x)

a11	a12	a13
a21	a22	a23
a31	a32	a33

NDA Math Determinants