latex \right\} not show up in pdf

Question

The following is a piece of LaTeX code displaying a function. But in the PDF file generated, the right curly bracket "}" does not show up at the end. If I replace \right\} with just \}, then the right bracket show up, but I want the larger one. One complication maybe that my equation is really long, so I had to break it up over multiple lines. Another problem I am having is that I want to line up my equation section, so I am using:

\subitem\space\space\space\space\space\space\space\space\space\space
\space\space\space\space\space\space\space\space \(` equation line `\) \\

There has to be a better way to do this.

Could anyone please point out to me how I can insert a large right curly bracket and have all the equation pieces line up based off of the left parenthesis "("?

Here's what I currently have:

And the code:

\documentclass[titlepage]{scrartcl}
\usepackage[utf8]{inputenc}
\setkomafont{disposition}{\normalfont\bfseries}
\usepackage{geometry}
\geometry{left=1in,right=1in,top=1in,bottom=1in}
\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{class}
\rhead{name}
\cfoot{\thepage} %center of the footer!
\renewcommand{\headrulewidth}{0.4pt}
\renewcommand{\footrulewidth}{0.4pt}
\begin{document}
\begin{description}
\item[\space\space\space\space\space\space\space ii.]Calculate the covariance matrix of each class (\(\Sigma_{1}, \Sigma_{2}\)) manually.
\\ \\
answer:
    \subitem \(\displaystyle \Sigma_{1} = \frac{1}{2-1}\left\{
    \left(\left[\begin{array}{c} 0.80 \\ 1.2\end{array}\right]-\left[\begin{array}{c} 1.0 \\ 1.375\end{array}\right]\right)
    \left(\left[\begin{array}{c} 0.80 \\ 1.2\end{array}\right]-\left[\begin{array}{c} 1.0 \\ 1.375\end{array}\right]\right)^{T} + \) 
    \subitem \space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \(
    \left(\left[\begin{array}{c} 0.90 \\ 1.4\end{array}\right]-\left[\begin{array}{c} 1.0 \\ 1.375\end{array}\right]\right)
    \left(\left[\begin{array}{c} 0.90 \\ 1.4\end{array}\right]-\left[\begin{array}{c} 1.0 \\ 1.375\end{array}\right]\right)^{T} + 
    \right\}\)
    \subitem \space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \(
    \left(\left[\begin{array}{c} 0.90 \\ 1.4\end{array}\right]-\left[\begin{array}{c} 1.0 \\ 1.375\end{array}\right]\right)
    \left(\left[\begin{array}{c} 0.90 \\ 1.4\end{array}\right]-\left[\begin{array}{c} 1.0 \\ 1.375\end{array}\right]\right)^{T} + 
    \right\}\)
    \subitem \space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \(
    \left(\left[\begin{array}{c} 0.90 \\ 1.4\end{array}\right]-\left[\begin{array}{c} 1.0 \\ 1.375\end{array}\right]\right)
    \left(\left[\begin{array}{c} 0.90 \\ 1.4\end{array}\right]-\left[\begin{array}{c} 1.0 \\ 1.375\end{array}\right]\right)^{T} \right\}\)
\end{description}
\end{document}

Answer 1

Suggestion to simplify your code.

\documentclass{scrartcl}
\usepackage{mathtools}

\newcommand*\bect[1]{\bectaux#1\relax} % bracketed vec
\def\bectaux#1,#2\relax{\begin{bmatrix}#1\\#2\end{bmatrix}}

\begin{document}
\[
  \Sigma_1 = \frac{1}{2-1}
    \!\begin{aligned}[t]
      \Biggl\{
        & \biggl( \bect{0.80,1.2} - \bect{1.0,1.375} \biggr) \biggl( \bect{0.80,1.2} - \bect{1.0,1.375} \biggr)^T + \\
        & \biggl( \bect{0.90,1.4} - \bect{1.0,1.375} \biggr) \biggl( \bect{0.90,1.4} - \bect{1.0,1.375} \biggr)^T + \\
        & \biggl( \bect{0.90,1.4} - \bect{1.0,1.375} \biggr) \biggl( \bect{0.90,1.4} - \bect{1.0,1.375} \biggr)^T + \\
        & \biggl( \bect{0.90,1.4} - \bect{1.0,1.375} \biggr) \biggl( \bect{0.90,1.4} - \bect{1.0,1.375} \biggr)^T
      \Biggr\}
    \end{aligned}
\]
\end{document}

Answer 2

There is no document command \subitem; it is defined but only for use in the index.¹

Also typing rows of \space commands is surely to be avoided. I can assure you that I may have typed \space in the body of a document maybe once or twice (except when the text requires a description of the \space command itself).

The solution I propose does not differ in a substantial way from Manuel's, but it features a couple of differences, the main one being that \left and \right are good here, where the number of rows in a \cvect is unknown (it's two, here, but I guess it could be more).

A trick for getting a better transposition symbol when next to a parenthesis is to use \!.

Alignment between the label and the word “Answer” can be obtained with the help of enumitem.

\documentclass[titlepage]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{geometry}

\setkomafont{disposition}{\normalfont\bfseries}
\geometry{left=1in,right=1in,top=1in,bottom=1in}

\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{enumitem}

\pagestyle{fancy}
\fancyhf{}
\fancyhead[L]{class}
\fancyhead[R]{name}
\fancyfoot[C]{\thepage} %center of the footer!
\renewcommand{\headrulewidth}{0.4pt}
\renewcommand{\footrulewidth}{0.4pt}

\newcommand{\cvect}[1]{\begin{bmatrix}#1\end{bmatrix}}
\newcommand{\nulldel}[1]{#1.\kern-\nulldelimiterspace}

\begin{document}

\begin{description}[leftmargin=1cm,itemindent=\labelsep]
\item[ii.] Calculate the covariance matrix of each class 
  (\(\Sigma_{1}, \Sigma_{2}\)) manually.\\*[\medskipamount]
Answer: \(
\begin{aligned}[t]
\Sigma_{1} = \frac{1}{2-1}\left\{ \vphantom{\cvect{0\\0}^{T}} \nulldel{\right}
  & \left(\cvect{0.80 \\ 1.2}-\cvect{1.0 \\ 1.375}\right)
    \left(\cvect{0.80 \\ 1.2}-\cvect{1.0 \\ 1.375}\right)^{\!T} + {} \\
  & \left(\cvect{0.90 \\ 1.4}-\cvect{1.0 \\ 1.375}\right)
    \left(\cvect{0.90 \\ 1.4}-\cvect{1.0 \\ 1.375}\right)^{\!T} + {} \\
  & \left(\cvect{0.90 \\ 1.4}-\cvect{1.0 \\ 1.375}\right)
    \left(\cvect{0.90 \\ 1.4}-\cvect{1.0 \\ 1.375}\right)^{\!T} + {} \\
  & \nulldel{\left} \left(\cvect{0.90 \\ 1.4}-\cvect{1.0 \\ 1.375}\right)
    \left(\cvect{0.90 \\ 1.4}-\cvect{1.0 \\ 1.375}\right)^{\!T}\, \right\}
\end{aligned} \)
\end{description}
\end{document}

_{¹ If you found \subitem in some guide, dispose of the guide in the best way possible, which involves the trash can. ;-)}