Question:
In the above question, $a_{11} C_{21}+a_{12} C_{22}+a_{13} C_{23}=$_______
Solution:
Given:
|A| = 5
As we know,
Sum of products of elements of row (or column) with their corresponding cofactors = Value of the determinant
and
Sum of products of elements of row (or column) with the cofactors of any other row (or column) = 0
Thus, $a_{11} C_{21}+a_{12} C_{22}+a_{13} C_{23}=0$
Hence, $a_{11} C_{21}+a_{12} C_{22}+a_{13} C_{23}=\underline{0}$.