Need help for an array or matrix

Question

I am trying to make an array or matrix to represent this matrix:

But unfortunately, I don't manage to do it (I even don't know if I should do it with an array or a pmatrix). So, if someone can help me...

Answer 1

This is a fairly faithful reproduction of the matrix using the nicematrix package.

The solid lines were drawn using the package's ability to insert tikz commands (with \CodeAfter) between the nodes it creates in the cells.

Requires compiling twice.

\documentclass[12pt,a4paper]{article}   

\usepackage{tikz} % needed <<<<<<<  
\usepackage{nicematrix} %    needed <<<<<<<

\begin{document}
    \setcounter{MaxMatrixCols}{20}
\[\tilde{A'} = \begin{pNiceMatrix}[first-row, cell-space-limits=5pt]
    &   &   &j_{1}  &   &       &   &j_{2}  &   &\cdots &       &j_{r-1}&       &\cdots &   &j_{r}  &   &       &   &\\
0   &-  &0  &1      &*  &\Cdots &*  &0      &*  &\Cdots &*      &0      &*      &\Cdots &*          &0      &*      &\Cdots &*      &b'_{1} \\
    &   &   &       &   &       &   &       &   &       &\Vdots &\Vdots &\Vdots &       &\Vdots     &\Vdots &\Vdots &       &\Vdots &       \\[-10pt]
    &   &0  &       &   &       &0  &1      &*  &       &       &       &       &       &           &       &       &       &       &b'_{2} \\
    &   &   &       &   &       &   &       &   &       &       &       &       &       &           &       &       &       &       &       \\[-10pt]
    &   &   &       &   &       &0  &       &   &       &       &       &       &       &           &       &       &       &       &b'_{3} \\
    &   &   &       &   &       &   &       &   &       &*      &0      &       &       &           &       &       &       &       &\Vdots \\
    &   &   &       &   &       &   &       &   &       &0      &1      &*      &\Cdots &*          &0      &       &       &       &b'_{r-1}\\
    &   &   &       &   &       &   &       &   &       &       &       &       &       &           &       &       &       &       &       \\[-10pt]       
    &   &   &       &   &       &   &       &   &       &0      &       &       &       &0          &1      &*      &\Cdots &*      &b'_{r} \\
    &   &   &       &   &       &   &       &   &       &       &       &       &       &           &       &       &       &       &       \\[-10pt]
    &   &   &       &   &       &   &       &   &       &       &       &       &       &0          &       &       &       &0      &b'_{r+1}\\
    &   &   &       &   &       &   &       &   &       &       &       &       &       &           &       &       &       &       &\Vdots \\
0   &   &   &       &   &       &   &       &   &       &       &       &       &       &           &       &       &       &0      &b'_{n} \\
\CodeAfter 
\tikz \draw  (2-|1.5) -- (13-|1.5); 
\tikz \draw  (3-|4) -- (3-|7); 
\tikz \draw  (5-|8) -- (5-|9); 
\tikz \draw  (7.5-|10) -- (7.5-|11); 
\tikz \draw  (9-|12) -- (9-|15); 
\tikz \draw  (11-|16) -- (11-|19); 
\tikz \draw  (13.5-|2) -- (13.5-|19); 
\tikz \draw  (2-|3.5) -- (2.5-|3.5); 
\tikz \draw  (4-|7.5) -- (4.5-|7.5); 
\tikz \draw  (8-|11.5) -- (8.5-|11.5); 
\tikz \draw  (10-|15.5) -- (10.5-|15.5); 
\tikz \draw  (12-|19.5) -- (13-|19.5); 
\end{pNiceMatrix}\]

\end{document}

Answer 2

Here is another solution with nicematrix.

\documentclass[a4paper,10pt]{article}
\usepackage{tikz}
\usepackage{nicematrix}

\begin{document}

\setcounter{MaxMatrixCols}{20}

\[
\renewcommand{\arraystretch}{1.4}
\widetilde{A'}=
\begin{pNiceMatrix}[nullify-dots,first-row]
 & &j_1& &      & &j_2& &\cdots       &      &j_{r-1}&      &\cdots&      &j_r   &      &      &      &\\ 
0&0&1  &*&\Cdots&*&0  &*&\hspace*{1cm}& *    &0     &*     &\Cdots&*     &0     &*     &\Cdots&*     &b_1' \\
 &0&   & &      &0&1  &*&             &\Vdots&\Vdots&\Vdots&      &\Vdots&\Vdots&\Vdots&      &\Vdots&b_2' \\
 & &   & &      &0&   & &             &      &      &      &      &      &      &      &      &      &b_3' \\
 & &   & &      & &   & &             &*     &0     &      &      &      &      &      &      &      &\Vdots \\
 & &   & &      & &   & &             &0     &1     &*     &\Cdots&*     &0     &      &      &      &b_{r-1}' \\
 & &   & &      & &   & &             &0     &      &      &      &0     &1     &*     &\Cdots&*     &b_r' \\
 & &   & &      & &   & &             &      &      &      &      &0     &      &      &      &0     &b_{r+1}' \\
 & &   & &      & &   & &             &      &      &      &      &      &      &      &      &      &\Vdots \\  
0& &   & &      & &   & &             &      &      &      &      &      &      &      &      &0     &b_n' 
\CodeAfter
  \begin{tikzpicture} [shorten < = 1mm, shorten > = 1mm]
  \draw (3-6) -- ++(1cm,0) ;
  \draw (2-6) -- (3-6) ;
  \draw (2-2) -- (2-6) ;
  \draw (1-2) -- (2-2) ;
  \draw (1-1) -- (1-2) ;
  \draw (1-1) -- (last-1) ;
  \draw (last-1) -- (last-18) ;
  \draw (last-18) -- (7-18) ;
  \draw (7-18) -- (7-14) ;
  \draw (7-14) -- (6-14) ;
  \draw (6-14) -- (6-10) ; 
  \draw (6-10) -- (5-10) ;
  \draw (5-10) -- ++(-1cm,0) ; 
  %
  \draw [dashed] (1-8) -- (1-10) ;
  \end{tikzpicture}
\end{pNiceMatrix}
\]

\end{document}

As usual with nicematrix, you need several compilations.