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Mathematics · JEE | DETERMINANTS
हिन्दीLet \( A = [a_{ij}] \) be a \( 3 \times 3 \) matrix with \( |A| = 7 \). Let \( A_{ij} \) be the cofactor of \( a_{ij} \). The value of the expression \( \sum_{j=1}^3 a_{1j} A_{1j} + \sum_{j=1}^3 a_{2j} A_{3j} \) is:
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Correct answer · Option D
\( 7 \)
Explanation
The first sum is the expansion along row 1: \( \sum_{j=1}^3 a_{1j} A_{1j} = |A| = 7 \). The second sum is the elements of row 2 multiplied by cofactors of row 3, which equals \( 0 \). Hence, \( 7 + 0 = 7 \).
