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Diffstat (limited to 'info/mathtrip/src/cramers.tex')
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diff --git a/info/mathtrip/src/cramers.tex b/info/mathtrip/src/cramers.tex new file mode 100644 index 0000000000..0175387442 --- /dev/null +++ b/info/mathtrip/src/cramers.tex @@ -0,0 +1,40 @@ +%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} |