User:Volker.haas/Test

Consider this swap of row $i$ with row $j$.

${\begin{array}{*{4}{rc}r}a_{1,1}x_{1}&+&a_{1,2}x_{2}&+&\cdots &&a_{1,n}x_{n}&=&d_{1}\\&&&&&&&\vdots \\a_{i,1}x_{1}&+&a_{i,2}x_{2}&+&\cdots &&a_{i,n}x_{n}&=&d_{i}\\&&&&&&&\vdots \\a_{j,1}x_{1}&+&a_{j,2}x_{2}&+&\cdots &&a_{j,n}x_{n}&=&d_{j}\\&&&&&&&\vdots \\a_{m,1}x_{1}&+&a_{m,2}x_{2}&+&\cdots &&a_{m,n}x_{n}&=&d_{m}\end{array}}{\xrightarrow[{}]{}}{\begin{array}{*{4}{rc}r}a_{1,1}x_{1}&+&a_{1,2}x_{2}&+&\cdots &&a_{1,n}x_{n}&=&d_{1}\\&&&&&&&\vdots \\a_{j,1}x_{1}&+&a_{j,2}x_{2}&+&\cdots &&a_{j,n}x_{n}&=&d_{j}\\&&&&&&&\vdots \\a_{i,1}x_{1}&+&a_{i,2}x_{2}&+&\cdots &&a_{i,n}x_{n}&=&d_{i}\\&&&&&&&\vdots \\a_{m,1}x_{1}&+&a_{m,2}x_{2}&+&\cdots &&a_{m,n}x_{n}&=&d_{m}\end{array}}$