Mathematics · JEE | DETERMINANTS

Consider the determinant layout illustrated for minor and cofactor expansion where element \( a_{21} \) is evaluated. What is the correct cofactor product term for \( a_{21} \) in a \( 3 \times 3 \) determinant expansion?

1. A
   \( a_{21} (-1)^{1+2} \begin{vmatrix} a_{22} & a_{23} \ a_{32} & a_{33} \end{vmatrix} \)
2. B
   \( a_{21} (-1)^{2+2} \begin{vmatrix} a_{11} & a_{13} \ a_{31} & a_{33} \end{vmatrix} \)
3. C
   \( a_{21} (-1)^{2+1} \begin{vmatrix} a_{12} & a_{13} \ a_{32} & a_{33} \end{vmatrix} \)
4. D
   \( a_{21} (-1)^{2+1} \begin{vmatrix} a_{11} & a_{12} \ a_{31} & a_{32} \end{vmatrix} \)