Determinants — Class 12 Maths Solution

The sum of products of elements of any row with the cofactors of corresponding elements is equal to value of the determinant.

Let $\Delta = \left| {\begin{array}{llllllllllllllllllll}{{a_{11}}}&{{a_{12}}}&{{a_{13}}}\\{{a_{21}}}&{{a_{22}}}&{{a_{23}}}\\{{a_{31}}}&{{a_{32}}}&{{a_{33}}}\end{array}} \right|$

Expanding along ${R_1}$,

$\Delta = {a_{11}}{A_{11}} + {a_{12}}{A_{12}} + {a_{13}}{A_{13}}$

$=$ Sum of products of elements of ${R_1}$ with their corresponding cofactors