row_additivity.md

行列式具有分行可加性，即

$$ \begin{align} &\begin{vmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ \vdots&\vdots&&\vdots\\ b_{l1}+c_{l1}&b_{l2}+c_{l2}&\cdots&b_{ln}+c_{ln}\\ \vdots&\vdots&&\vdots\\ a_{n1}&a_{n2}&\cdots&a_{nn} \end{vmatrix}\\ = &\begin{vmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ \vdots&\vdots&&\vdots\\ b_{l1}&b_{l2}&\cdots&b_{ln}\\ \vdots&\vdots&&\vdots\\ a_{n1}&a_{n2}&\cdots&a_{nn} \end{vmatrix}+ \begin{vmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ \vdots&\vdots&&\vdots\\ c_{l1}&c_{l2}&\cdots&c_{ln}\\ \vdots&\vdots&&\vdots\\ a_{n1}&a_{n2}&\cdots&a_{nn} \end{vmatrix} \end{align} $$