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fix text going outside of column
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dariusptrs committed Oct 25, 2024
1 parent c9a6a20 commit 1c01100
Showing 1 changed file with 4 additions and 1 deletion.
5 changes: 4 additions & 1 deletion Lineare-Algebra.tex
Original file line number Diff line number Diff line change
Expand Up @@ -195,7 +195,10 @@ \subsection{Determinante}
\draw[thin, blue] (extended-1-2.north east) -- (m-3-3.south west);
\end{tikzpicture}
\]
$=\textcolor{red!70!white}{a_{11}a_{22}a_{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}}\textcolor{blue!70!white}{-a_{12}a_{21}a_{33}-a_{11}a_{23}a_{32}-a_{13}a_{22}a_{31}}$
\resizebox{\columnwidth}{!}{$
=\textcolor{red!70!white}{a_{11}a_{22}a_{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}}%
\textcolor{blue!70!white}{-a_{12}a_{21}a_{33}-a_{11}a_{23}a_{32}-a_{13}a_{22}a_{31}}
$}
\item $\det\begin{pmatrix}A&0\\C&D\end{pmatrix}=\det\begin{pmatrix}A&B\\0&D\end{pmatrix}=\det(A)\cdot\det(D)$
\item $\begin{vmatrix}\lambda_1&&* \\ &\ddots& \\ 0&&\lambda_n \end{vmatrix} = \lambda_1\cdot \ldots\cdot \lambda_n = \begin{vmatrix} \lambda_1&&0 \\ &\ddots& \\ *&&\lambda_n \end{vmatrix}$
\item $A=B \cdot C \quad \Rightarrow \quad |A|=|B| \cdot |C|$
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