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I am currently working on a lab report where I have to explain the Gaussian Elimination Method for a matrix. As part of my explanation, I want to circle/oval portions of a matrix.

Is there any way to circle the main diagonal of a matrix or a corner of it? Pics below with examples. I am thinking I may have to use a put structure on top of an array/matrix environment but I do not know how to do that.

EDIT: Here's what I currently have to generate the matrix that I drew on in the pictures:

usepackage[utf8]{inputenc}

usepackage{indentfirst}

usepackage{graphicx}

usepackage{setspace}

usepackage[numbers]{natbib}

usepackage [autostyle, english = american]{csquotes}

MakeOuterQuote{"}

usepackage{layout}

usepackage[title]{appendix}

usepackage[justification=centering]{caption}

usepackage{titlesec}

usepackage[percent]{overpic}

usepackage{amsmath}

usepackage{systeme}

usepackage{blkarray, bigstrut}



...



begin{center}

    begin{blockarray}{cccc}

        begin{block}{ [ ccc| c ]}

            bigstrut[t]

             1 & -1 &  3 & -3 \

            -1 &  0 & -2 &  1 \

             2 &  2 &  4 &  0 bigstrut[b] \

        end{block}

    end{blockarray}

end{center}

Here is a possible way using tikzmark.

documentclass{article}

usepackage[utf8]{inputenc}

usepackage{blkarray, bigstrut}

usepackage{tikz}

usetikzlibrary{tikzmark,calc,fit}

begin{document}

begin{center}

    begin{blockarray}{cccc}

        begin{block}{ [ ccc| c ]}

            bigstrut[t]

             tikzmarknode{A11}{1} & -1 &  3 & -3 \

            -1 &  0 & -2 &  1 \

             2 &  2 &  tikzmarknode{A33}{4} &  0 bigstrut[b] \

        end{block}

    end{blockarray}

end{center}

begin{tikzpicture}[remember picture,overlay]

 draw let p1=($(A33)-(A11)$),n1={atan2(y1,x1)} in 

 node[rotate fit=n1,fit=(A11) (A33),draw,rounded corners,inner sep=2pt]{};

end{tikzpicture}



begin{center}

    begin{blockarray}{cccc}

        begin{block}{ [ ccc| c ]}

            bigstrut[t]

             1 & -1 &  3 & -3 \

            tikzmarknode{B21}{-1} &  0 & -2 &  1 \

             tikzmarknode{B31}{2} &  tikzmarknode{B32}{2} &  4 &  0 bigstrut[b] \

        end{block}

    end{blockarray}

end{center}

begin{tikzpicture}[remember picture,overlay]

node[fit=(B21) (B31) (B32),inner sep=2pt] (FB){};

path (FB.south east) arc(-90:45:4pt) coordinate(aux1);

draw (aux1) arc(45:-90:4pt) -- ([xshift=4pt]FB.south west)

arc(-90:-180:4pt) -- (FB.north west) arc(180:45:4pt) -- cycle;

end{tikzpicture}



begin{center}

    begin{blockarray}{cccc}

        begin{block}{ [ ccc| c ]}

            bigstrut[t]

             1 & tikzmarknode{C12}{-1} &  tikzmarknode{C13}{3} & -3 \

             -1 &  0 & tikzmarknode{C23}{-2} &  1 \

             2 &  2 &  4 &  0 bigstrut[b] \

        end{block}

    end{blockarray}

end{center}

begin{tikzpicture}[remember picture,overlay]

node[fit=(C12) (C23) (C13),inner sep=2pt] (FC){};

path (FC.north west) arc(90:225:4pt) coordinate(aux2);

draw (aux2) arc(225:90:4pt) -- ([xshift=-4pt]FC.north east)

arc(90:0:4pt) -- (FC.south east) arc(0:-135:4pt) -- cycle;

end{tikzpicture}

end{document}