How to write Gaussian reduction?

Question

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 '19 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 '19 at 21:49

Franck Pastor · Answer 1 · 2019-10-13T18:46:52.123

8

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}

edited Oct 13 '19 at 18:46

answered Oct 13 '19 at 17:04

Franck Pastor

18,756

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 '19 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 '19 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 '19 at 18:41
@Moh18 I suggest opening another subject to address this new problem :-) – Franck Pastor Oct 13 '19 at 18:42
@FranckPastor https://tex.stackexchange.com/questions/512111/aligning-and-spaces-for-negative-numbers-and-fractions-in-a-matrix – Moh18 Oct 13 '19 at 19:08
@FranckPastor 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 '19 at 03:54
@barbarabeeton 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 '19 at 03:54
@Moh18 -- For expressions over/under xrightarrow, look at the instructions and examples in section 4.9, "Extensible arrows", in the amsmath user guide (texdoc amsldoc). Also, the answers here do show the proper input method. – barbara beeton Oct 14 '19 at 15:58

Sebastiano · Answer 2 · 2020-07-18T21:24:34.680

EDIT: 2020-7-18 Another option could be using the nicematrix package (see the recent version and the comment of the author of the 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).

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 '19 at 03:52
@Moh18 Hi, I have done an addendum for your request. My best regards, — Sebastiano, Oct 14 '19 at 20:58
In this answer, since version 5.0 of nicematrix one must write cccc|l instead of CCCC|L in the preambles of {NiceArray} (but there is an option for backward compatibility). — F. Pantigny, Jul 18 '20 at 21:15
@F.Pantigny I'll correct that immediately and thank you immensely. — Sebastiano, Jul 18 '20 at 21:17

How to write Gaussian reduction?

2 Answers2

ADDENDUM by comment of the user