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+%This command provides the cramers rule in the column 1
+%of the third horizontal part of page 10
+%
+%This command has one parameter:
+% 1) The width of the line used to typeset the formulae
+\newcommand\TTenCramer[1]{%
+ \parbox[t]{#1}{%
+ \TTenCramerFontSize
+ \DisplaySpace{\TTenDisplaySpace}{\TTenDisplayShortSpace}
+ \noindent If we have equations:%
+ \[\begin{array}{l%Col 2 plus sign
+ @{\hspace{.2em}}c@{\hspace{.2em}}% Col 3
+ l%Col 4, \cdot
+ wc{4em}%Col 5, plus sign
+ @{\hspace{.2em}}c@{\hspace{.2em}}% Col 6
+ l%Col 7 equal sign
+ @{\hspace{.2em}}c@{\hspace{.2em}}% Col 8
+ l}
+
+ a_{1,1} x_1 &+& a_{1,2} x_2& \makebox[2em][c]{$\cdots$} &+& a_{1,n} x_n &=& b_1 \\
+ a_{2,1} x_1 &+& a_{2,2} x_2& \makebox[2em][c]{$\cdots$} &+& a_{2,n} x_n &=& b_2 \\
+ & & & & & & & \\
+ & & & \vdots & & & & \\
+ & & & & & & & \\
+ a_{n,1} x_1 &+& a_{n,2} x_2& \makebox[2em][c]{$\cdots$} &+& a_{n,n} x_n &=& b_n \\
+ \end{array}\]
+
+ \AdjustSpace{3ex plus .5 ex minus 1ex}
+
+ Let $A = (a_{i,j})$ and $B$ be the column matrix $(b_i)$.
+ Then there is a unique solution iff $\det A \neq 0$.
+ Let $A_i$ be $A$ with column $i$ replaced by $B$.
+ Then
+ \begin{displaymath}
+ x_i = \frac{\det A_i}{\det A}.
+ \end{displaymath}
+ }%
+}
+%The command containing the title of this part
+\newcommand\TTenCramersTitle{Cramer's rule}