[Tex/LaTex] 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}