How to: Encircle a row/column in a matrix (for Laplace expansion)

Question

How to encircle the second row in this step of Laplace expansion or to illustrate that point in a different way?

\begin{align*}
    \left| \begin{pmatrix}{1 & 4 & -2 & 7 & 1 \\ 0 & 3 & 0 & 0 & 0 \\ 2 & -3 & 0 & 8 & 0 \\ -7 & 3 & -1 & 3 & -2 \\ 0 & 2 & 0 & -4 & 0} \end{pmatrix}  \right| = +3 \cdot \left| \begin{pmatrix}{1 & -2 & 7 & 1 \\ 2 & 0 & 8 & 0 \\ -7 & -1 & 3 & -2 \\ 0 & 0 & -4 & 0} \end{pmatrix} \right|
\end{align*}

There are certainly different ways to underline the steps of the Laplace expansion, but I did not found them yet. Additionally it would be great to incorporate the 'chessboard pattern' and so on.

Thanks

Could you check whether a few old posts can help? For example: Array cell highlighting tikz, Highlight elements in the matrix. — Claudio Fiandrino, Oct 20 '15 at 10:05
I was hoping that there might be a way around TikZ, because it's too complicated for my purpose (too many matrices). I am flexible on the highlights of a matrix, maybe someone got a nice idea for native implementation? — Mac, Oct 20 '15 at 10:29

score 2 · Answer 1 · answered Oct 20 '15 at 12:50

This is rather simple to do with pstricks: nodes at the beginning and end of the row or column, then a box-type node connection:

\documentclass[x11names]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath,array}
\usepackage{pst-node}
\usepackage{auto-pst-pdf}

\begin{document}
\begin{pspicture}
\begin{align*}
    \left| \begin{pmatrix}1 & 4 & -2 & 7 & 1 \\ \Rnode{B}{0} & \color{OrangeRed1}3 & 0 & 0 & \Rnode{E}{0}\\ 2 & -3 & 0 & 8 & 0 \\ -7 & 3 & -1 & 3 & -2 \\ 0 & 2 & 0 & -4 & 0 \end{pmatrix} \right| = {\color{OrangeRed1}{+3}} \cdot \left| \begin{pmatrix}1 & -2 & 7 & 1 \\ 2 & 0 & 8 & 0 \\ -7 & -1 & 3 & -2 \\ 0 & 0 & -4 & 0 \end{pmatrix} \right|
\end{align*}
\ncbox[boxsize=1.33ex, nodesep=0.9ex, linecolor=LightSteelBlue2, linewidth=0.6pt, linearc=0.05]{B}{E}
\end{pspicture}
\end{document}

This somehow does not work for me, maybe it's in conflict with some of my tikz packages? Or my scrartcl-class? — Mac, Oct 21 '15 at 10:33
Normally it shouldn't. However, don't forget, in order to make pdflatex work with pstricks, you must compile with the --write18 switch (MiKTeX) or -shell-escape (TeX Live, MacTeX). — Bernard, Oct 21 '15 at 13:26

score 1 · Answer 2 · answered Oct 20 '15 at 11:06

You can try with addpath command from easybmat

\documentclass{article}
\usepackage{lmodern}
\usepackage{amsmath,array}
\usepackage{easybmat}

\begin{document}
\[
\begin{vmatrix}
\begin{pmatrix}
\begin{BMAT}(b){rrrrr}{ccccc}
1 & 4 & -2 & 7 & 1 \\ 
0 & 3 & 0 & 0 & 0 \\ 
2 & -3 & 0 & 8 & 0 \\ 
-7 & 3 & -1 & 3 & -2 \\ 
0 & 2 & 0 & -4 & 0 
\addpath{(0,1,0)rrrrrullllld}
\end{BMAT}  
\end{pmatrix}
\end{vmatrix}
\]
\end{document}

How to: Encircle a row/column in a matrix (for Laplace expansion)

2 Answers2