In array right braces don't look

Question

In following Tex script right braces aren't looked.

\documentclass[a4paper,12pt]{article}
\usepackage[turkish]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{enumitem}
\usepackage[shortlabels]{enumerate}
\usepackage{mathptmx}
\usepackage{setspace}
\makeatletter
\renewcommand*\env@matrix[1][\arraystretch]{%
    \edef\arraystretch{#1}%
    \hskip -\arraycolsep
    \let\@ifnextchar\new@ifnextchar
    \array{*\c@MaxMatrixCols c}}
\makeatother
\newcommand*\circled[1]{\tikz[baseline=(char.base)]{
        \node[shape=circle,draw,inner sep=2pt] (char) {#1};}}
\usepackage{mathptmx}
\begin{document}
\[\begin{array}{*{9}{@{}c@{}}}
max\left\{(a_{11}+x_1) & {},{} & max(a_{12}+x_1) &{},{} & \cdots & {},{} & max(a_{1n}+x_n)\right\} & {}\mathrel{=}{} & b_1 \\
max\left\{(a_{21}x_1) & , & max(a_{22}x_2) & , & \cdots & , & max(a_{2n}x_n)\right\} & = & b_2 \\
\vdots    &   & \vdots    &   &        &   & \vdots    &   & \vdots \\
max\left\{(a_{m1}x_1) & , & max(a_{m2}x_2) & , & \cdots & , & max(a_{mn}x_n)\right\} & = & b_m \\
\end{array}\]
\end{document}

Answer 1

Just remove \left and \right

\[\begin{array}{*{9}{@{}c@{}}}
max\{(a_{11}+x_1) & {},{} & max(a_{12}+x_1) &{},{} & \cdots & {},{} & max(a_{1n}+x_n)\} & {}\mathrel{=}{} & b_1 \\
max\{(a_{21}x_1) & , & max(a_{22}x_2) & , & \cdots & , & max(a_{2n}x_n)\} & = & b_2 \\
\vdots    &   & \vdots    &   &        &   & \vdots    &   & \vdots \\
max\{(a_{m1}x_1) & , & max(a_{m2}x_2) & , & \cdots & , & max(a_{mn}x_n)\} & = & b_m \\
\end{array}\]

If you want to grow up your brackets jyou can use \big, \bigg, \Big, etc.