Math & Science ⇒ Rule of Sarrus

[Math12345]

I have a problem! I need to write the Sarrus rule for 3x3 determinant, indicating additional two columns (to the right of the matrix) and diagonal lines for positive and negative products. How should I proceed? any idea?
Thanks in advance and greetings

[localghost]

A usual environment like array won't help you on here. The pgf/tikZ package can help you to construct a matrix with the necessary properties and the capability to connect the matrix elements with lines (or arrows). Let's take the example from the Wikipedia article [1].

Code: Select all

Code, edit and compile here:

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\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{calc,matrix}
\begin{document}
  \begin{tikzpicture}
    \matrix [%
      matrix of math nodes,
      column sep=1em,
      row sep=1em
    ] (sarrus) {%
      a_{11} & a_{12} & a_{13} & a_{11} & a_{12} \\
      a_{21} & a_{22} & a_{23} & a_{21} & a_{22} \\
      a_{31} & a_{32} & a_{33} & a_{31} & a_{32} \\
    }; 
    \path ($(sarrus-1-3.north east)+(0.5em,0)$) edge[dotted] ($(sarrus-3-3.south east)+(0.5em,0)$)
          (sarrus-1-1)                          edge         (sarrus-2-2)
          (sarrus-2-2)                          edge         (sarrus-3-3)
          (sarrus-1-2)                          edge         (sarrus-2-3)
          (sarrus-2-3)                          edge         (sarrus-3-4)
          (sarrus-1-3)                          edge         (sarrus-2-4)
          (sarrus-2-4)                          edge         (sarrus-3-5)
          (sarrus-3-1)                          edge[dashed] (sarrus-2-2)
          (sarrus-2-2)                          edge[dashed] (sarrus-1-3)
          (sarrus-3-2)                          edge[dashed] (sarrus-2-3)
          (sarrus-2-3)                          edge[dashed] (sarrus-1-4)
          (sarrus-3-3)                          edge[dashed] (sarrus-2-4)
          (sarrus-2-4)                          edge[dashed] (sarrus-1-5);
    \foreach \c in {1,2,3} {\node[anchor=south] at (sarrus-1-\c.north) {$+$};};
    \foreach \c in {1,2,3} {\node[anchor=north] at (sarrus-3-\c.south) {$-$};};
  \end{tikzpicture}
\end{document}
 
 
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Run LaTeX here

For further adjustments and modifications take a look at the very comprehensive package manual.

[1] Rule of Sarrus — Wikipedia, the free encyclopedia


Best regards and welcome to the board
Thorsten

[Math12345]

Thanks Torsten for the code.
However, when trying to run it I get the message

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l.3 \usetikzlibrary{calc,matrix}
Please type another input file name:
 
 
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And then nothing more....
I am not so skilled in Latex and am not sure how to ommit it.

Best, and thanks.

[localghost]

Submit the complete log file produced by my example code by upload to the forum server.

[Stefan Kottwitz]

You could check if you use the current version of pgf/TikZ, which is 2.10. If not, I recommend updating it.

Stefan

[Math12345]

Thanks Torsten and Stefan,
I noticed that I didn't have PGF/TikZ installed on my Mac at all. I downloaded version 2.10 but here is no information what so ever how to install it or were to put the files. As soon as I solve this problem I will check the code from Thorsten. If you have an idea how to handle the installation, please advice (I use TexShop)

All the best.

[localghost]

[…] If you have an idea how to handle the installation, please advice (I use TexShop) […]

I guess that the TeX Live Utility will be very helpful in this regard. I don't know how to get it. Perhaps it is already installed with MacTeX.

[frabjous]

Don't try to install it manually. Use the package manager of your TeX distribution. E.g., try (from a terminal):

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sudo tlmgr install pgf
 
 
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You might also look into the possibility of a GUI frontend for your distribution; some info here for MacTeX.

[Math12345]

IT WORKS !!!!!!
I'd like to say THANK YOU to all wonderful contributors!