How to cross a row in matrix with a line?

You can use tikz for this. Probably not the finest answer possible, but works for me:

\documentclass{article}
\usepackage{tikz}
\newcommand{\pmark}[1]{\begin{tikzpicture}[overlay,remember picture]\node(#1)at (-1em,.7ex){};\end{tikzpicture}}
\newcommand{\smark}[1]{\begin{tikzpicture}[overlay,remember picture]\draw(#1)--(0,.7ex);\end{tikzpicture}}
\begin{document}
$$\begin{array}{cccc|c}
a&b&bc&d&f\\\hline
0\pmark{a}&0&1&1&1\smark{a}\\
0&0&0&1&0\\
0&0&1&1&1\\
\end{array}$$
$f=\overline{a}\wedge\overline{b}\wedge c\wedge+\dots$
\end{document}