%This command provides the text about matrix in the first part

%This command provides the text about matrix in the first part
%of the column 2 of the page 4.
%
%The macro has one parameter
% 1) The width allowed for the text
\newcommand\TFourMatrix[1]{%
\parbox[t]{#1}{%
\DisplaySpace{\TFourDisplaySpace}{\TFourDisplayShortSpace}
%The column is narrow, text looks better ragged right
\raggedright

\TFourTitle{Multiplication:}
\begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
\Fm{C = A \cdot B},
\Fm{c_{i,j} = \sum_{k=1}^n a_{i,k} b_{k,j}}.
\end{DisplayFormulae}

\TFourTitle{Determinants:}
$\det A \neq 0$ iff $A$ is non-singular.
\begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
\Fm{\det A \cdot B = \det A \cdot \det B},
\Fm{\det A = \sum_\pi \prod_{i=1}^n \sign(\pi) a_{i,\pi(i)}}.
\end{DisplayFormulae}

\TFourTitle{$2 \times 2$ and $3 \times 3$ determinant:}
\AdjustSpace{1ex plus .5ex minus .2ex}
\begin{DisplayFormulae}{1}{0pt}{5ex plus 1ex minus 1ex}{\SmallChar}{\StyleWithoutNumber}
\Fm{\begin{bmatrix}
a &b \\
c &d \\
\end{bmatrix} = a d - b c}
%Second Equation, matrix 3x3
\def\FirstPart{A=\begin{bmatrix}%
a &b &c \\
d &e &f \\
g &h &i \\
\end{bmatrix}}
\FmPartA{\FirstPart =
g\begin{bmatrix}%
b &c \\
e &f \\
\end{bmatrix}
-h \begin{bmatrix}%
a &c \\
d &f \\
\end{bmatrix}+}
\FmPartB{\FirstPart =}{\enspace i \begin{bmatrix}%
a &b \\
d &e \\
\end{bmatrix}}
\Fm{\det A=a e i + b f g + c d h -c e g - f h a - i b d}
\end{DisplayFormulae}

\TFourTitle{Permanents:}
\begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber}
\Fm{\perm A = \sum_\pi \prod_{i=1}^n a_{i,\pi(i)}}.
\end{DisplayFormulae}
}%
}