IMathAS-libretexts

What row operation does multiplication by the following matrix perform?

\displaystyle {\left[\begin{array}{ccccc} {1}&{0}&{0}&{0}&{0}\\{0}&{1}&{0}&{0}&{0}\\{0}&{0}&{1}&{0}&{0}\\{0}&{0}&{0}&{1}&{0}\\{0}&{0}&{0}&-{1}&{1}\end{array}\right]}

$\displaystyle {R}_{{2}}\leftrightarrow{R}_{{5}}$
$\displaystyle {R}_{{1}}\leftrightarrow{R}_{{2}}$
$\displaystyle -{1}{R}_{{5}}\rightarrow{R}_{{5}}$
$\displaystyle -{2}{R}_{{5}}\rightarrow{R}_{{5}}$
$\displaystyle -{4}{R}_{{5}}\rightarrow{R}_{{5}}$
$\displaystyle -{3}{R}_{{2}}+{R}_{{5}}\rightarrow{R}_{{5}}$
$\displaystyle -{1}{R}_{{4}}+{R}_{{5}}\rightarrow{R}_{{5}}$
$\displaystyle {5}{R}_{{3}}+{R}_{{5}}\rightarrow{R}_{{5}}$
$\displaystyle {R}_{{4}}\leftrightarrow{R}_{{5}}$