How can I draw a vertical Line In Matrix and add Arrows?

Question

Here is a pic of this.

Is there away to type this thing out?

Answer 1

One way is to use array:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\[
\left[\begin{array}{@{} rrr|rrr @{\,}}
 1 &  2 & -1 & 1 & 0 & 0  \\
-2 &  0 &  1 & 0 & 1 & 0  \\
 1 & -1 &  0 & 0 & 0 & 1  \\
\end{array}\right]
\]
\end{document}

Answer 2

This is based on this answer, which borrows from this post, and this answer, which uses this answer. The purpose is to align the minus signs and numbers nicely.

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{% https://tex.stackexchange.com/a/33523
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{#1}}
\makeatother
\usepackage{array}
\makeatletter
\def\CheckMinus\ignorespaces{\@ifnextchar-{}{\phantom{-}}}
\makeatother
\newcolumntype{J}{>{\CheckMinus}l}

\begin{document}
\begin{equation}
  \begin{bmatrix}[JJJ|JJJ]
 1 &  2 & -1 & 1 & 0 & 0  \\
-2 &  0 &  1 & 0 & 1 & 0  \\
 1 & -1 &  0 & 0 & 0 & 1  \\
  \end{bmatrix}\xrightarrow{R_1-R_3}
\end{equation}
\end{document}

Answer 3

A simple solution with delarray:

\documentclass{article}
\usepackage{amsmath}
\usepackage{delarray}

\begin{document}

\[ \begin{array}[c][{rrr|rrr}]
1 & 2 & -1 & 1 & 0 & 0 \\
-2 & 0 & 1 & 0 & 1 & 0 \\
 1 & -1 & 0 & 0 & 0 & 1 
\end{array}\xrightarrow{R_1-R_3}
\]

\end{document}