IMathAS-libretexts

What row operation will transform

\displaystyle {\left[\begin{array}{cccc} {1}&{7}&{4}&-{1}\\{3}&{2}&-{9}&{4}\\-{1}&-{6}&-{5}&-{1}\end{array}\right]}

into

\displaystyle {\left[\begin{array}{cccc} {1}&{7}&{4}&-{1}\\{3}&{2}&-{9}&{4}\\{0}&{1}&-{1}&-{2}\end{array}\right]}

?

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