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} $$