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Mathematics · JEE | DETERMINANTS
हिन्दीLet \( \Delta = \begin{vmatrix} 1 & x & yz \ 1 & y & zx \ 1 & z & xy \end{vmatrix} \). If the expansion of \( \Delta \) using cofactors of the third column yields \( \lambda (x-y)(y-z)(z-x) \), then the value of \( \lambda \) is:
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Correct answer · Option C
\( 1 \)
Explanation
Performing \( R_2 \to R_2 - R_1 \) and \( R_3 \to R_3 - R_1 \): \( \Delta = \begin{vmatrix} 1 & x & yz \ 0 & y-x & z(x-y) \ 0 & z-x & y(x-z) \end{vmatrix} = (y-x)(z-x) \begin{vmatrix} 1 & -z \ 1 & -y \end{vmatrix} = (y-x)(z-x)(z-y) = (x-y)(y-z)(z-x) \). Thus \( \lambda = 1 \).
