How to write a matrix and a text above the aj,i columns (on top) and in front of (side) the n- rows?

Question

This is what I tried, but failed to produce the desired result. Please Help! "LaTex Environment"

\documentclass[12pt, a4paper, oneside]{article}
\hyphenation{Fortran hy-phen-ation} % Specify custom hyphenation points in words with dashes where you would like hyphenation to occur, or alternatively, don't put any dashes in a word to stop hyphenation altogether
%\usepackage[T1]{fontenc} % output font encoding for international characters
\usepackage[english]{babel} % English language/hyphenation
\usepackage{lmodern}
\usepackage{textcomp}
\usepackage[utf8x]{inputenc}
%\usepackage{kpfonts}
%\DeclareUnicodeCharacter{211D} {\mathbb{R}}
%\DeclarationUnicodeCharacter{00A0} {}
%\DeclarationUnicodeCharacter{00A0} {~}
%\usepackage{fourier}
%\usepackage{lipsum} % Used for inserting dummy 'Lorem ipsum' text into the template
\usepackage{xfrac}
\usepackage{sectsty} % Allows customizing section commands
%\allsectionsfont{\centering \normalfont\scshape} % Make all sections centered, the default font and small caps
\usepackage{multirow}
\usepackage{tikz}
\usepackage{booktabs}         %to use \toprule and \bottomrule without error message
\usepackage{pgfplots}         %to plot figure
\usepackage{threeparttable} 
\usepackage{booktabs}         %to use \toprule and \bottomrule without error message
\usepackage{pgfplots}   
\pgfplotsset{compat=1.5}
\usepackage{subfigure}        % to add subfigures
\usepackage{gensymb}
%\usepackage[none]{hyphenat}  %to prevent word breaking
\usepackage{siunitx}
\usepackage{caption}
\usepackage{booktabs} 
\newcommand*{\head}[1]{\textbf{#1}}%  to make heads of table in BOLD, it is used with booktabs package and \head
\usepackage{cleveref}
\usepackage{url} \makeatletter \g@addto@macro{\UrlBreaks}{\UrlOrds} \makeatother
\usepackage[justification=centering]{caption}
\PassOptionsToPackage{hyphens}{url}
%\usepackage{hyperref}
\usepackage{float}
%\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
%\usepackage[a4paper, portrait, margin=1in]{geometry}
\usepackage{adjustbox}
\usepackage{tabularx}
\usepackage{pgfplots, pgfplotstable}
\usepackage{booktabs,csvsimple}
\usepackage{pdflscape}
%% packages
%\input{settings/packages}
%% page setting
%\input{settings/pages}
%% own comments
%\usepackage[margin=1in]{geometry}
\usepackage{amsmath, amsfonts, amsthm} % needed for command eqref or Math packages
\usepackage{amssymb} % needed for math fonts
%\usepackage{hyperref}
\usepackage[
    colorlinks=true
   ,breaklinks
   %, ngerman
    ] {hyperref} % needed for creating hyperlinks in the docuent, the option colorlink=true gets rid of the awful boxes, breaklinks breaks lonk links (list of figures), and the ngerman sets everthing for german s default hyperlink languages.
%\usepackage[hyphenbreaks]{breakurl} 
\usepackage{xcolor}
\definecolor {c1}{rgb}{0,0, 1} % blue
\definecolor {c2}{rgb}{0.3,0.3, 0.9} % light blue
\definecolor {c3}{rgb}{0.3,0.3, 0.9} % red blue
\hypersetup{
   linkcolor={c1}, % internal links
    citecolor={c2}, % citations 
    urlcolor={c3} % external links/urls
}

%\usepackage[round, authoryear]{natbib} % needed for abbrvant bibliography style
%\usepackage[nottoc]{tocbibind} % needed for displaying bibliography and other in the table of contents
\usepackage{graphicx} % needed for\includegraphics
%\imp{graphicx}
\usepackage{longtable} % needed for long tables over pages
\usepackage{bigstrut} % needed for the  command \bigstrut
\usepackage{enumerate} % needed for some options in enumerate
%\usepackage{todonotes} % needed for todos
\usepackage{makeidx}  % needed for creating an index
\usepackage{xcolor}
\usepackage{blindtext} % needed for creating dummy text passage
\usepackage{lipsum}
\usepackage{setspace}
\usepackage{fancyhdr}
\usepackage{float}
\usepackage[nottoc, notlot, notlof]{tocbibind}
%% page settings%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[top=2cm, bottom=1.8cm, left=2.5cm, right=2.5cm]{geometry} % needed for page border stteings 
\parindent=0cm % for spece of first line of new text block
\sloppy % for writing with hypenless justification (tries to)
%\hyphenation {} % use hypenation of tolerance parameters, http://www.jr-x.de/publikationen/latex/tipps/zeilenumbruch_html
%\hyphenpenalty=10000
%\exhyphenpenalty=10000
%\usepackage{fancyhdr} % Custom headers and footers
%\usepackage{fourier} % Use the Adobe Utopia font for the document - comment this line to return to the LaTeX default
%\usepackage[english]{babel} % English language/hyphenation
%\usepackage{lipsum} % Used for inserting dummy 'Lorem ipsum' text into the template
%\usepackage{sectsty} % Allows customizing section commands
%\allsectionsfont{\centering \normalfont\scshape} % Make all sections centered, the default 

%\usepackage[round, authoryear]{natbib} % needed for cite and abbrvnat bibliograph style
\usepackage[nottoc]{tocbibind} % needed for displayng bibliography and other in the able of contents
%\usepackage{figures}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\pagestyle{fancy}
\fancyhf{}
%\cfoot{\thepage}
\fancyhead {}
\fancyfoot{}
\fancyhead[L]{\slshape \MakeUppercase {Multidimensional Poverty Index (MPI) in Ethiopia}}
%\fancyhead[R]{\slshape WELDESLASSIE HAILAI}
\fancyfoot[C]{\thepage}
%\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}

%\setlength{\parindent}{4em} %This is going to change the width of that indent
%\setlength{\parskip}{1em} % This is going to change the amount of spacing in between your paragraphes if you want that
\renewcommand{\baselinestretch}{1.5}%This affects the in spacing of my paragraphes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\graphicspath{ {images/} }
\begin{titlepage}
\begin{center}
\vspace*{1cm}
\pagestyle{empty}
\pagestyle{plain}
......
$$
\begin{array}{cc}
\text{Income} & \text{Years of Education} & \text{Improved Sanitation} & \text {Access to improved Electricity &\\
\begin{bmatrix}
900 & 10 & Yes & Yes\\
300 & 15 & No  & Yes \\
400 & 9  & No  & No \\
800 & 12 & Yes & Yes\\
1000& 13 & No  &  No
\end{bmatrix} &
\begin{small}
Person_1\\
Person_2\\
Person_3\\
Person_4\\
Person_5\\
\end{small}
\end{array}
 $$
......
\end {doocument}

Answer 1

Here is a solution with blkarray and makecell . The latter allows line breaks and a common formatting of cells introduced by the command \thead and \makecell. I took the opportunity to partly clean the preamble of the unnecessary packages and to remove double-loading of packages.

\documentclass[12pt, a4paper, oneside]{article}
\usepackage[english]{babel} % English language/hyphenation
\usepackage{lmodern}
\usepackage{textcomp}
\usepackage[utf8]{inputenc}
\usepackage{xfrac}
\usepackage{multirow}
\usepackage{tikz}
\usepackage{pgfplots, pgfplotstable} %to plot figure
\usepackage{threeparttable}
\pgfplotsset{compat=1.5}
\usepackage{siunitx}
\usepackage{booktabs}
\newcommand*{\head}[1]{\textbf{#1}}% to make heads of table in BOLD, it is used with booktabs package and \head
\usepackage{url} \makeatletter \g@addto@macro{\UrlBreaks}{\UrlOrds} \makeatother
\usepackage[justification=centering]{caption}
\usepackage{float}
%\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
%\usepackage[a4paper, portrait, margin=1in]{geometry}
\usepackage{adjustbox}
\usepackage{tabularx, makecell}
\usepackage{booktabs,csvsimple}
\usepackage{pdflscape}
\usepackage{amsmath, amsfonts, amsthm} % needed for command eqref or Math packages
\usepackage{amssymb} % needed for math fonts
\usepackage[
    colorlinks=true
   ,breaklinks
   %, ngerman
    ] {hyperref} % needed for creating hyperlinks in the docuent, the option colorlink=true gets rid of the awful boxes, breaklinks breaks lonk links (list of figures), and the ngerman sets everthing for german s default hyperlink languages.
%\usepackage[hyphenbreaks]{breakurl}
\usepackage{cleveref}
\usepackage{xcolor}
\definecolor {c1}{rgb}{0,0, 1} % blue
\definecolor {c2}{rgb}{0.3,0.3, 0.9} % light blue
\definecolor {c3}{rgb}{0.3,0.3, 0.9} % red blue
\hypersetup{
   linkcolor={c1}, % internal links
    citecolor={c2}, % citations
    urlcolor={c3} % external links/urls
}
\usepackage{graphicx} % needed for\includegraphics
\usepackage{longtable} % needed for long tables over pages
\usepackage{bigstrut} % needed for the command \bigstrut
\usepackage{enumerate} % needed for some options in enumerate
\usepackage{blkarray}
\usepackage{lipsum}
\usepackage{setspace}
\usepackage{fancyhdr}
%% page settings%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[top=2cm, bottom=1.8cm, left=2.5cm, right=2.5cm]{geometry} % needed for page border stteings
\parindent=0cm % for spece of first line of new text block
\sloppy % for writing with hypenless justification (tries to)
\pagestyle{fancy}
\fancyhf{}
\fancyhead {}
\fancyfoot{}
\fancyhead[L]{\slshape \MakeUppercase {Multidimensional Poverty Index (MPI) in Ethiopia}}
%\fancyhead[R]{\slshape WELDESLASSIE HAILAI}
\fancyfoot[C]{\thepage}
%\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\renewcommand{\baselinestretch}{1.5}%This affects the in spacing of my paragraphes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand\theadset{\renewcommand{\arraystretch}{0.6}}
\renewcommand\theadfont{\small}
\renewcommand\theadalign{bc}

\begin{document}

\begin{center}
\begin{blockarray}{rcccc}
 & \thead{Income} & \thead{Years of \\Education} & \thead{Improved\\ Sanitation} & \thead{Access to\\ improved \\ Electricity}\\
\begin{block}{>{\small}r[cccc]}
Person\textsubscript{1} & 900 & 10 & Yes & Yes\\
Person\textsubscript{2}& 300 & 15 & No & Yes \\
Person\textsubscript{3} & 400 & 9 & No & No \\
Person\textsubscript{4} & 800 & 12 & Yes & Yes\\
Person\textsubscript{5} & 1000& 13 & No & No\\
\end{block}
\end{blockarray}
\end{center}

\end{document} 

Answer 2

This solution overlays left and right brackets on the tabular using tikz. I removed all of your packages as they were irrelevant to the problem.

\documentclass{standalone}
\usepackage{tikz}

\newlength{\tempwidth}
\newlength{\tempheight}

\begin{document}
\begin{tabular}{rcccc}
 & Income & Years of Education & Improved Sanitation & Access to improved Electricity \\
Person\textsubscript{1} & \tikz[remember picture]{\node[inner sep=0pt](First){900};} & 10 & Yes & Yes\\
Person\textsubscript{2}& 300 & 15 & No & Yes \\
Person\textsubscript{3} & 400 & 9 & No & No \\
Person\textsubscript{4} & 800 & 12 & Yes & Yes\\
Person\textsubscript{5} & 1000& 13 & No & \tikz[remember picture]{\node[inner sep=0pt](Last){No};}\\
\end{tabular}
\begin{tikzpicture}[remember picture,overlay]
  \pgfextractx{\tempwidth}{\pgfpointdiff{\pgfpointanchor{First}{west}}{\pgfpointanchor{Last}{east}}}%
  \pgfextracty{\tempheight}{\pgfpointdiff{\pgfpointanchor{Last}{south}}{\pgfpointanchor{First}{north}}}%
  \path (First.north west) -- (Last.south east) node[midway] {$\displaystyle \left[ \rule[-0.5\tempheight]{0pt}{\tempheight}% vertical strut
    \rule{\tempwidth}{0pt} \right]$};% horizontal strut
\end{tikzpicture}
\end{document} 

---

Personally, I don't get the reason for adding brackets. OTOH, it would be nice to have the numbers be right aligned and still be centered (more or less), hence the \makeboxs.

There are a number of ways to compute the widths for \makebox, including using a one column tabular {@{}r@{}}.

\documentclass{standalone}

\newlength{\firstcol}% width of first column (numbers only)
\newlength{\secondcol}% width of second column (numbers only)

\settowidth{\firstcol}{1000}% widest text
\settowidth{\secondcol}{15}

\begin{document}
\begin{tabular}{r|cccc}
 & Income & Years of Education & Improved Sanitation & Access to improved Electricity \\
\hline
Person\textsubscript{1} & \makebox[\firstcol][r]{900} & \makebox[\secondcol][r]{10} &Yes & Yes\\
Person\textsubscript{2}& \makebox[\firstcol][r]{300} & \makebox[\secondcol][r]{15} & No & Yes \\
Person\textsubscript{3} & \makebox[\firstcol][r]{400} & \makebox[\secondcol][r]{9} & No & No \\
Person\textsubscript{4} & \makebox[\firstcol][r]{800} & \makebox[\secondcol][r]{12} & Yes & Yes\\
Person\textsubscript{5} & \makebox[\firstcol][r]{1000} & \makebox[\secondcol][r]{13} & No & No \\
\end{tabular}
\end{document}