Problems using `\left\{` in array environment

Question

I am trying to define a matrix in segments by enclosing the entries of the matrix in boxes, and also using the open and closed braces to label those segments. So far I have developed the following code to do this.

\documentclass[a4,12pt]{report}

\usepackage{multirow}

\begin{document}

\[
  A =
    \left(
      \begin{array}{rrrrrl}
          \cline{2-4} \cline{5-5}
        \multirow{2}{*}{$B \{$} &
          \multicolumn{1}{|r}{1} & 2 & \multicolumn{1}{r|}{-4} & \multicolumn{1}{|r|}{1} & \multirow{2}{*}{$\} \hat{\mathbf{b}}^{T}$} \\
          & \multicolumn{1}{|r}{2} & -5 & \multicolumn{1}{r|}{-3} & \multicolumn{1}{|r|}{-3} & \\
          \cline{2-4} \cline{5-5}
        \hat{\mathbf{c}} \{  & \multicolumn{1}{|r}{-6} & -3 & \multicolumn{1}{r|}{0} & \multicolumn{1}{|r|}{5} & \} a_{n-1,n} \\
          \cline{2-4} \cline{5-5}
        \hat{\mathbf{d}} \{ & \multicolumn{1}{|r}{-6} &  7 & \multicolumn{1}{r|}{0} & \multicolumn{1}{|r|}{-8} & \} a_{n,n} \\
          \cline{2-4} \cline{5-5}
      \end{array}
    \right)
\]


\end{document}

This produces the following output:

What I want to do is expand the left and right brace in the first and last columns to line up with the rows that have been segmented. One way of doing this is to use the \left\{ and \right\} LaTeX commands. The problem is that when I do this, I get the following LaTeX error:

! Missing \right.  inserted.
<inserted text>
                \right .
l.12         \multirow{2}{*}{$B \left\{$}
                                          &
?

Also, what I would like to do is separate the segments using individual boxes, rather than adjoining boxes as above. Any ideas on how to do this would be very much appreciated.

Answer 1

I took @mico's answer and added hhline

\documentclass[a4paper,12pt]{report}
\usepackage{multirow,hhline}
\begin{document}
  \[
  A =
  \left(
  \begin{array}{r|rrr||r|l}
    \hhline{~|---||-|~}
    \multirow{2}{*}{$B \bigg\{$} 
    & 1 & 2 & -4 & 1 & 
    \multirow{2}{*}{$\bigg\} \hat{\mathbf{b}}^{T}$} \\
    & 2 & -5 & -3 & -3 & \\
    \hhline{~:===::=:~}
    \hat{\mathbf{c}} \{  & -6 & -3 & 0 & 5 & \} a_{n-1,n} \\
    \hhline{~:===::=:~}
    \hat{\mathbf{d}} \{ & -6 &  7 & 0 & -8 & \} a_{n,n} \\
    \hhline{~|---||-|~}
  \end{array}
  \right)
  \]
\end{document}

Answer 2

Here's a solution using the tried and tested \tikzmark idea, first show cased in Andrew Stacey's answer to

Adding a large brace next to a body of text

The code below uses a version modified from Peter Grill's answer to

Box around a few items in an itemize environment

My solution is a little bit fiddly- there's a bit of manual column and row spacing, and a couple of uses of \vphantom so that instead of using \bigg you can use \left\{...\right. but the output is (I hope) quite pleasing.

\documentclass[a4,12pt]{report}

\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{multirow}

\newcommand{\DrawBox}[3][]{%
    \tikz[overlay,remember picture]{
        \coordinate (RightPoint) at (#3.east);
    \draw[red,#1]
      ($(#2)+(-.5em,.9em)$) rectangle
      ($(RightPoint)+(0.2em,-0.3em)$);}
}

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}

\begin{document}

\[
  A =
    \left(
    \begin{array}{r@{\hspace{.2cm}}c@{}rrr@{\hspace{.5cm}}r@{}rl}
       \multirow{2}{*}{$B \left\{\vphantom{\begin{array}{c}1\\2\end{array}}\right.$} 
                                &\tikzmark{left1}   & 1   & 2  & -4                     &\tikzmark{left3}   & 1  & 
                                \multirow{2}{*}{$\left.\vphantom{\begin{array}{c}1\\2\end{array}}\right\} \hat{\mathbf{b}}^{T}$} \\
                                &                   & 2   & -5 & -3\tikzmark{right1}    &                   &-3 \tikzmark{right3}   & \\[5pt]
        \hat{\mathbf{c}} \{     &\tikzmark{left2}   & -6  & -3 & 0 \tikzmark{right2}    &\tikzmark{left4}   & 5  \tikzmark{right4}  &\}a_{n-1,n} \\[5pt]
        \hat{\mathbf{d}} \{     &\tikzmark{left5}   & -6  &  7 & 0 \tikzmark{right5}    &\tikzmark{left6}   & -8 \tikzmark{right6}  & \} a_{n,n} \\
      \end{array}
    \right)
\]

\DrawBox[thick,green,fill=yellow,fill opacity=0.1]{left1}{right1}
\DrawBox[thick,blue]{left2}{right2}
\DrawBox[thick,red]{left3}{right3}
\DrawBox[thick,purple]{left4}{right4}
\DrawBox[thick,yellow]{left5}{right5}
\DrawBox[thick,orange]{left6}{right6}

\end{document}

Answer 3

You could use the explicit size statement \bigg in order to set the size of the left and right curly braces, as is shown in the following modified form of your MWE. To get the arrays display with a little gap while using the \cline command, it's necessary to break them up into two separteI've also simplified the code to get rid of most of the \multicolumn statements and combining the various paired \cline statements.

\documentclass[a4paper,12pt]{report}
\usepackage{multirow}
\begin{document}      
  \[
  A =
  \left(
  \begin{array}{r|rrr|}
    \cline{2-4} 
    \multirow{2}{*}{$B \bigg\{$} 
    & 1 &  2 & -4  \\ 
    & 2 & -5 & -3 \\
    \cline{2-4} 
    \hat{\mathbf{c}} \{  & -6 & -3 & 0 \\
    \cline{2-4}
    \hat{\mathbf{d}} \{  & -6 &  7 & 0 \\
    \cline{2-4} 
  \end{array}
  \right. \kern-3pt \left. % use \kern-3pt to reduce distance between arrays
  \begin{array}{|r|l}
    \cline{1-1}
     1 & \multirow{2}{*}{$\bigg\} \hat{\mathbf{b}}^{T}$} \\
    -3 & \\
    \cline{1-1}
     5 & \} a_{n-1,n} \\
    \cline{1-1}
    -8 & \} a_{n,n} \vphantom{\hat{\mathbf{d}}}\\  
        % the \vphantom is needed to equalize the heights of the 
        % third rows across the two arrays
    \cline{1-1}
  \end{array}
  \right)
  \]
\end{document}