Diskutim:Hipi Zhdripi i Matematikës/1118

${\begin{matrix}a_{11}&a_{12}&a_{1r}\\a_{21}&a_{22}&a_{2r}\\\vdots \\a_{r1}&a_{r2}&a_{rr}\\\end{matrix}}$ ${\begin{matrix}a_{1,r+1}&\dots &a_{1r}\\a_{2,r+1}&\dots &a_{2r}\\\vdots \\a_{r,r+1}&\dots &a_{rr}\\\end{matrix}}$
${\begin{matrix}a_{r+1,r}&a_{r+1,r}&a_{1r}&a_{1,r+1}&\dots &a_{r+1,n}\\\vdots \\a_{m1}&a_{m2}&a_{mr}&a_{m,r+1}&\dots &a_{mn}\\\end{matrix}}$

${\begin{matrix}a_{11}&a_{12}&a_{1r}&a_{1,r+1}&\dots &a_{1r}\\a_{21}&a_{22}&a_{2r}&a_{2,r+1}&\dots &a_{2r}\\\vdots &&&\vdots \\a_{r1}&a_{r2}&a_{rr}&a_{r,r+1}&\dots &a_{rr}\\a_{r+1,r}&a_{r+1,r}&a_{1r}&a_{1,r+1}&\dots &a_{r+1,n}\\\vdots \\a_{m1}&a_{m2}&a_{mr}&a_{m,r+1}&\dots &a_{mn}\\\end{matrix}}$

prov

${\begin{matrix}a_{11}&a_{12}&a_{1r}&a_{1,r+1}&\dots &a_{1r}\\a_{21}&a_{22}&a_{2r}&a_{2,r+1}&\dots &a_{2r}\\\vdots &&&\vdots \\a_{r1}&a_{r2}&a_{rr}&a_{r,r+1}&\dots &a_{rr}\\a_{r+1,r}&a_{r+1,r}&a_{1r}&a_{1,r+1}&\dots &a_{r+1,n}\\\vdots \\a_{m1}&a_{m2}&a_{mr}&a_{m,r+1}&\dots &a_{mn}\\\end{matrix}}$