4

I want to know how to draw the three (in)equality signs vertically like shown in the figure.

enter image description here

4

You can set these as part of a regular array:

enter image description here

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\[
  \begin{pmatrix}
     3 & 2 & -2 & 7 &  4 \\
    -2 & 4 &  1 & 3 & -2 \\
     1 & 5 &  1 & 0 &  3
  \end{pmatrix}
  \begin{pmatrix}
    x_1 \\ x_2 \\ x_3 \\ x_4 \\ x_5
  \end{pmatrix}
  \begin{array}{@{}c@{}}
    {}\geq{} \\ \leq \\ =
  \end{array}
  \begin{pmatrix}
    1 \\ -3 \\ 4
  \end{pmatrix}
\]

\end{document}

The use of {}\geq{} (or at least a surrounding group set for one of the relations) ensures that the spacing is as expected; that of \mathrel.

2

It's a simple matrix, but embedded in \mathrel:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\relstack}[1]{\mathrel{\begin{matrix}#1\end{matrix}}}

\begin{document}

\[
\begin{pmatrix}
3 & 2 & -2 & 7 & 4 \\
-2 & 4 & 1 & 3 & -2 \\
1 & 5 & 1 & 0 & 3
\end{pmatrix}
\begin{pmatrix}
x_1 \\ x_2 \\ x_3 \\ x_4 \\ x_5
\end{pmatrix}
\relstack{\ge \\ \le \\ =}
\begin{pmatrix}
1 \\ -3 \\ 4
\end{pmatrix}
\]

\end{document}

enter image description here

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