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+%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}
+ }%
+}