Btukfyl

During preparing a note about elementary row operations, I did the following as similar as I had found through the site:

documentclass[a4paper,12pt]{book}‎

usepackage{amsmath,amssymb,amsthm,amsfonts}‎ 

begin{document}‎‎

‎‎begin{pmatrix}

‎2‎‎ & 1 \ 

1 & -5\‎

3 & circled{7} 

end{pmatrix}‎

‎‎xrightarrow ‎{‎tfrac{-12}{2}‎R_1+ R_3‎mapsto ‎R_3}‎‎

begin{pmatrix}

‎2‎‎ & 1 \ 

1 & -5\‎

-21 & circled{5-‎}‎ 

end{pmatrix}

‎end{document}‎

‎
Is it possible to do it as the picture?

I think, If I can do that, they will be illustrated nicely.

Since you didn't provide a complete MWE, I used a circled command found here.

By the way, the parts already written in your MWE don't exactly correspond to the image, I've replicated the image.

Is this what you what to achieve?

documentclass[a4paper,12pt]{book}

usepackage{amsmath,amssymb,amsthm,amsfonts}

usepackage{tikz}

newcommand*circled[1]{tikz[baseline=(A.base)]{node[circle,draw,inner sep=1](A){$#1$};}}% code from: https://tex.stackexchange.com/a/304891/101651

usepackage{array}

newcolumntype{R}{>{$}r<{$}}

usepackage{booktabs}

begin{document}

[

begin{pmatrix}

2 & 1 \ 

1 & -5\

3 & circled{7} 

end{pmatrix}

xrightarrow[scriptsizebegin{tabular}{R!{:}RR}

   -12R_{1}  &  -24 & -12\

    R_{3} & 3 & 7\

    cmidrule(lr){2-3}

    text{(new) } R_{3} & -21 & -5

end{tabular}]{-12R_1+ R_3mapsto R_3}

begin{pmatrix}

2 & 1 \ 

1 & -5\

-2 & circled{-5} 

end{pmatrix}

]

end{document}

documentclass[a4paper,12pt]{book}

usepackage{amsmath,amssymb,amsthm,amsfonts}

usepackage{array}

begin{document}

[

left(begin{array}{cc}

    2 & 1\

    1 & -5\

    3 & 7

end{array}right)xrightarrow[

    begin{scriptsize}

    begin{array}{rrr}

        -12R_1: & -24 & -12\

        R_3: & 3 & 7\

        cline{2-3}

        text{(new) }R_3: & -21 & -5

    end{array}

    end{scriptsize}

]{-12R_1+R_3rightarrow R_3}left(begin{array}{cc}

    2 & 1\

    1 & -5\

    -21 & -5

end{array}right)

]

end{document}