I have a determinant $ \begin{vmatrix} a_{11}\ a_{12}\ a_{13} .... a_{1n}\\ a_{21}\ a_{22}\ a_{23} .... a_{2n}\\ .................\\ .................\\ a_{n1}\ a_{n2}\ a_{n3} .... a_{nn}\\ \end{vmatrix} =|A| $ now I have replaced let's say the second column with $ \begin{vmatrix}c_1\\ c_2\\ .\\.\\c_n\\ \end{vmatrix} $
such that it becomes
$ \begin{vmatrix} a_{11}\ c_{1}\ a_{13} .... a_{1n}\\ a_{21}\ c_{2}\ a_{23} .... a_{2n}\\ .................\\ .................\\ a_{n1}\ c_{n}\ a_{n3} .... a_{nn}\\ \end{vmatrix} =?$
I want to know the fastest way to do it.