# How to write Gaussian reduction?

I am still a newbie in LaTeX and I am trying to write something like that but I couldn't find how to do so.

Is there an efficient way to write this and if I have multiple steps to show in the reduction how do I align them?

Thanks!

• Welcome to TeX.SE. Please do tell us what you've tried so far and where you feel you're getting stuck. – Mico Oct 13 at 17:03
• Minor nit: I’m more used to seeing columns of numbers align right than left or center. Sebastiano’s answer already matches the output you want, so +1. – Davislor Oct 14 at 21:49

I would use something like this:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
$\left( \begin{array}{*4{l}|l} 1 & 1 & 1 & 1 & b_1\\ 0 & 2 & 3 & 3 & b_2-b_1\\ 0 & 2 & 3 & 3 & b_3-b_1\\ 0 & 4 & 4 & 5 & b_4-b_1\\ \end{array} \right) \xrightarrow[L_4 \rightarrow L_4-2L_2]{L_3 \rightarrow L_3-L_2} \left( \begin{array}{*4{l}|l} 1 & 1 & 1 & 1 & b_1\\ 0 & 2 & 3 & 3 & b_2-b_1\\ 0 & 0 & 0 & 0 & b_3-b_1-b_2\\ 0 & 0 & -2 & -1 & b_4+b_1-2b_2\\ \end{array} \right).$
\end{document}


• Since you're using array, you might consider aligning the first four columns as 4r instead of 4l so that the minus signs don't shove the negative values out of line. – barbara beeton Oct 13 at 17:40
• Thanks! However, I have another question. I am trying to write this [\left(\begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix},\begin{pmatrix} 0 \\ \frac{1}{4} \\ \frac{1}{2} \\ 0 \end{pmatrix},\begin{pmatrix} 1 \\ \frac{1}{4} \\ -\frac{1}{2} \\ 0 \end{pmatrix},\begin{pmatrix} 0 \\ -\frac{1}{2\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0\end{pmatrix}\right)] but is there a way to align number with \begin{pmatrix} and the fractions are a little too close of each others (I don't know how to space them) – Moh18 Oct 13 at 18:12
• @barbarabeeton this is what I would have done for myself, but I wanted to reproduce what Moh18 wanted. – Franck Pastor Oct 13 at 18:41
• @Moh18 I suggest opening another subject to address this new problem :-) – Franck Pastor Oct 13 at 18:42
• @FranckPastor tex.stackexchange.com/questions/512111/… – Moh18 Oct 13 at 19:08

Another option could be using the nicematrix package. Here there is my approach:

\documentclass[a4paper,12pt]{article}
\usepackage{nicematrix}
\usepackage{mathtools}
\begin{document}
$\left(\begin{NiceArray}{CCCC|L} 1 & 1 & 1 & 1 & b_1\\ 0 & 2 & 3 & 3 & b_2-b_1\\ 0 & 2 & 3 & 3 & b_3-b_1\\ 0 & 4 & 4 & 5 & b_4-b_1 \end{NiceArray}\right) \xrightarrow[L_4 \rightarrow L_4-2L_2]{L_3 \rightarrow L_3-L_2} \left(\begin{NiceArray}{CCCC|L} 1 & 1 & 1 & 1 & b_1\\ 0 & 2 & 3 & 3 & b_2-b_1\\ 0 & 0 & 0 & 0 & b_3-b_1-b_2\\ 0 & 0 & -2 & -1 & b_4+b_1-2b_2\\ \end{NiceArray}\right).$
\end{document}


## ADDENDUM by comment of the user

There are several procedures to have, for example, on the same arrow your reductions: see this link how to force text to write in two or more lines in overset command for example.

\documentclass[a4paper,12pt]{article}
\usepackage{nicematrix}
\usepackage{mathtools}
\begin{document}
$\left(\begin{NiceArray}{CCCC|L} 1 & 1 & 1 & 1 & b_1\\ 0 & 2 & 3 & 3 & b_2-b_1\\ 0 & 2 & 3 & 3 & b_3-b_1\\ 0 & 4 & 4 & 5 & b_4-b_1 \end{NiceArray}\right) \xrightarrow{ \begin{subarray}{l} L_4 \rightarrow L_4-2L_2\\ L_3 \rightarrow L_3-L_2\\ L_2 \rightarrow \frac{1}{2} %%% here you can add other steps \end{subarray} } \left(\begin{NiceArray}{CCCC|L} 1 & 1 & 1 & 1 & b_1\\ 0 & 2 & 3 & 3 & b_2-b_1\\ 0 & 0 & 0 & 0 & b_3-b_1-b_2\\ 0 & 0 & -2 & -1 & b_4+b_1-2b_2\\ \end{NiceArray}\right).$
\end{document}


You, if it is possible, read the guide of nicematrix package you could get a better result (see the image of the guide to pag. 18, for example).

• Thank you for you response! – Moh18 Oct 13 at 19:15
• @Moh18 I'm happy when I help someone. Glad I helped you. – Sebastiano Oct 13 at 19:16
• If, between the two matrices, I have to show more that two steps. For example, $L_4 \rightarrow L_4-2L_2$ ,$L_3 \rightarrow L_3-L_2$,$L_2 \rightarrow \frac{1}{2}$. How can I write them under or over the $\xrightarrow$? – Moh18 Oct 14 at 3:52
• @Moh18 Hi, I have done an addendum for your request. My best regards, – Sebastiano Oct 14 at 20:58