Matrices with Annotations

Question

Do you have any suggestion how to make such formula? Or maybe I need to draw them somehow?

Big thanks for any hints!

Answer 1

I suggest using nicematrix.

\documentclass{article}
\usepackage{nicematrix, tikz}
\begin{document}
[
\begin{pNiceArray}{rrrrr}[first-row]
\downarrow && \downarrow && \downarrow\
1 & 3 & 3 & 2 & 1\
2 & 6 & 9 & 5 & 2\
-1 & -3 & 3 & 0 & 1\
3 & 9 & 6 & 5 & 2
\end{pNiceArray}
\sim
\begin{pNiceArray}{rrrrr}[first-row]
\downarrow && \downarrow && \downarrow\
1 & 3 & 3 & 2 & 1\
0 & 0 & 3 & 1 & 0\
0 & 0 & 0 & 0 & 2\
0 & 0 & 0 & 0 & 0
\CodeAfter
\tikz \draw (2-|1)--(2-|3)--(3-|3)--(3-|5)--(4-|5)--(4-|6);
\end{pNiceArray}
]
\end{document}

If you want to tighten up the spacing in the first matrix, you can change the first line to \begin{pNiceArray}{@{\,}r@{\;}rrrr}[first-row]