Matrix change row or column background

Question

I have a matrix shown below. I would like to have the whole row green rather than only the cells ... how can I do that?

\begin{equation}\label{eq:appendrow}
\newcommand\x{\times}
\newcommand\y{\colorbox{mygreen}{$1$}}
  \left(\begin{array}{cccc}
    \x  & \x  & \x & \x \\
    0   & \x  & \x & \x \\
    0   & 0   & \x & \x \\
    0   & 0   & 0  & \x \\
    \y  & \y  & \y & \y \\
  \end{array}\right)
\end{equation}

and the output is:

Answer 1

You can use \rowcolor, \columncolor, and \cellcolor from the colortbl package, loaded in my example through the xcolor package:

\documentclass{article}
\usepackage{amsmath}
\usepackage[table]{xcolor}

\newcommand\x{\times}
\newcommand\y{\cellcolor{green!10}}

\begin{document}

\begin{equation}\label{eq:appendrow}
  \left(\begin{array}{cccc}
    \rowcolor{red!20}
    \x  & \x  & \x & \x \\
    0   & \x  & \x & \x \\
   \rowcolor{blue!20}
    0   & 0   & \x & \x \\
    0   & 0   & 0  & \x \\
    \y a  &  b  & \y c &  d\\
  \end{array}\right)
\end{equation}

\begin{equation}
  \left(\begin{array}{>{\columncolor{olive!20}}cc>{\columncolor{yellow!20}}cc}
    \x  & \x  & \x & \x \\
    0   & \x  & \x & \x \\
    0   & 0   & \x & \x \\
    0   & 0   & 0  & \x \\
    a  & b  & c & d \\
  \end{array}\right)
\end{equation}

\end{document}

Answer 2

Another approach could be using the hf-tikz package.

Example:

\documentclass{article}
\usepackage{amsmath}

\newcommand\x{\times}

\usepackage[customcolors]{hf-tikz}
\hfsetfillcolor{green!50}
\hfsetbordercolor{white}

\begin{document}

\begin{equation}\label{eq:appendrow}
  \left(\begin{array}{cccc}
    \x  & \x  & \x & \x \\
    0   & \x  & \x & \x \\
    0   & 0   & \x & \x \\
    0   & 0   & 0  & \x \\
    \tikzmarkin{color this row} a  &  b  &  c &  d \tikzmarkend{color this row}\\
  \end{array}\right)
\end{equation}

\begin{equation}\label{eq:appendcol}
  \left(\begin{array}{cccc}
    \x  & \x  & \tikzmarkin{color this column}(0.15,-0.15)(-0.1,0.3) \x & \x \\
    0   & \x  & \x & \x \\
    0   & 0   & \x & \x \\
    0   & 0   & 0  & \x \\
    a  &  b  &  c  \tikzmarkend{color this column} &  d \\
  \end{array}\right)
\end{equation}

\end{document}

Result:

Explanation

The approach is based on the famous \tikzmark macro by Andrew Stacey and Peter Grill. One should just mark the starting and ending position of the area to be highlighted by means of the commands \tikzmarkin and \tikzmarkend. This area could be customized by extend markers passing to the \tikzmarkin the coordinates that represent the shift of markers from the default value. For example:

\tikzmarkin{color this column}(0.15,-0.15)(-0.1,0.3)