I have this
output (without the annotations and am somewhat confused about the aligning. This is the code for this example:
\documentclass[10pt, a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[headheight=0cm,bindingoffset=0cm]{geometry}
\usepackage{amssymb}
\usepackage[fleqn,leqno]{amsmath}
\setlength{\mathindent}{\labelsep}
\addtolength{\mathindent}{1.165ex}
\openup 1.25\jot
% increase matriced formating options https://tex.stackexchange.com/questions/2233/whats-the-best-way-make-an-augmented-coefficient-matrix
\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{
\hskip -\arraycolsep
\let\@ifnextchar\new@ifnextchar
\array{#1}
}
\makeatother
\begin{document}
\begin{align*}
&\begin{pmatrix}[ccc|c]
x & x & x & x \\
x & x & x & x \\
x & x & x & x \\
\end{pmatrix} &\rightarrow
\begin{pmatrix}[ccc|c]
x & x & x & x \\
x & x & x & x \\
x & x & x & x \\
\end{pmatrix}\\
column1&column2&column3\\
%
&\begin{aligned}
&\text{text} \\
&r=-2 \\
&\begin{pmatrix}[ccc|c]
1 & x & x & x \\
0 & x & x & x \\
0 & x & x & x \\
\end{pmatrix} &\rightarrow L=\varnothing \\
%
&\text{text:} \\
&r=0 \\
&\begin{pmatrix}[ccc|c]
x & x & x & x \\
x & x & x & x \\
x & x & x & x \\
\end{pmatrix} &\rightarrow L=
\begin{pmatrix}[ccc|c]
x \\
x \\
x \\
\end{pmatrix}\\
&\text{text:} \\
&r=1 \\
&\begin{pmatrix}[ccc|c]
x & x & x & x \\
x & x & x & x \\
x & x & x & x \\
\end{pmatrix} &\rightarrow L=
\begin{pmatrix}[ccc|c]
x \\
x \\
x \\
\end{pmatrix}\\
\end{aligned}\\
&\text{text:}\\
&\begin{pmatrix}[ccc|c]
x & x & x & x \\
x & x & x & x \\
x & x & x & x \\
\end{pmatrix} &\rightarrow L=
\begin{pmatrix}[ccc|c]
x \\
x \\
x \\
\end{pmatrix}\\
\end{align*}
\end{document}
I'd expect, that the first, second and forth elements would be aligned to where the aligned output ends (horizontally) and that the arrows inside the aligned environment would be horizontally aligned (which is in case of the first arrow not the case).
Somehow I don't get why this isn't what I'd expect it to look like, please help.

shortintertext... – oliversm May 07 '20 at 13:23