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Mathematics · JEE | DETERMINANTS
हिन्दीLet \( A = \begin{pmatrix} 1 & 0 & 4 \ 3 & 5 & -1 \ 0 & 1 & 2 \end{pmatrix} \). If \( A_{ij} \) is the cofactor of \( a_{ij} \), then the value of \( A_{13} + A_{23} + A_{33} \) is equal to:
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Correct answer · Option C
\( 7 \)
Explanation
\( A_{13} = (-1)^{1+3} (3\times 1 - 5\times 0) = 3 \); \( A_{23} = (-1)^{2+3} (1\times 1 - 0\times 0) = -1 \); \( A_{33} = (-1)^{3+3} (1\times 5 - 0\times 3) = 5 \). Thus, \( 3 + (-1) + 5 = 7 \).
