I need to add some straight lines inside a matrix to indicate labeling of rows, like this:

How do I do that?
Leaders is optimal for this situation. amsmath provides \hdotsfor{<cols>} that draws a dotted leader across <cols> columns. It is also possible to overlay a row number by setting that specific row twice (once with \hdotsfor and once with a row number, say). I've also added \numberrowwithline{<cols>}{<stuff>} that draws a line (instead of dots) as a dash leader, and inserts <stuff> in the middle of <cols> columns. The default space on either side is \fboxsep.
The following is a modified example, taken from Herbert's mathmode document:

\documentclass{article}
\usepackage{xcolor}% http://ctan.org/pkg/xcolor
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\newcommand{\numberrowwithline}[2]{%
\multicolumn{#1}c%
{\xleaders\hbox{-\kern-1pt}\hfill\kern\fboxsep%
#2\hspace*{\fboxsep}%
\xleaders\hbox{-\kern-1pt}\hfill\kern0pt%
}%
}
\begin{document}
\begin{equation}
\underline{A}=\left[\begin{array}{ccccccc}
a_{11} & a_{12} & 0 & \ldots & \ldots & \ldots & 0 \\
a_{21} & a_{22} & a_{23} & 0 & \ldots & \ldots & 0 \\
0 & a_{32} & a_{33} & a_{34} & 0 & \ldots & 0 \\
\hdotsfor{7} \\
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\
\hdotsfor{7} \\[-\normalbaselineskip]
\multicolumn{7}{c}{\colorbox{white}{\ $R_n$\ }} \\
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\
\numberrowwithline{7}{R_i} \\
0 & \ldots & 0 & a_{n-2,n-3} & a_{n-2,n-2} & a_{n-2,n-1} & 0 \\
0 & \ldots & \ldots & 0 & q_{n-1,n-2} & a_{n-1,n-1} & a_{n-1,n} \\
0 & \ldots & \ldots & \ldots & 0 & a_{n,n-1} & a_{nn}
\end{array}\right]
\end{equation}
\end{document}
With the addition of xhfill you can go crazy with the colours and types of leaders. See the xhfill documentation for the different styles of lines as a sample.
With nicematrix.
\documentclass{article}
\usepackage{xcolor}
\usepackage{nicematrix,tikz}
\begin{document}
$\begin{bNiceArray}{cc@{\hspace{7mm}}ccc}
a_{11} &a_{12} & \Cdots[shorten=5pt] & a_{1,n-1} & a_{1n} \
\Cdots[line-style=solid] && R_2 & \Cdots[line-style=solid] \
&& \vdots \
\Cdots[line-style=solid] && R_n & \Cdots[line-style=solid] \
\end{bNiceArray}$
\end{document}