%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}
   }%
}
