From c9a6a209b3df47203d3be3849101034b436cb6b1 Mon Sep 17 00:00:00 2001
From: Darius Peters <38152878+dariusptrs@users.noreply.github.com>
Date: Fri, 25 Oct 2024 17:03:43 +0200
Subject: [PATCH] add colors to 3x3 det

---
 Lineare-Algebra.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lineare-Algebra.tex b/Lineare-Algebra.tex
index 3123e83..e51a8a7 100644
--- a/Lineare-Algebra.tex
+++ b/Lineare-Algebra.tex
@@ -195,7 +195,7 @@ \subsection{Determinante}
     \draw[thin, blue] (extended-1-2.north east) -- (m-3-3.south west);
 \end{tikzpicture}
 \]
-$=a_{11}a_{22}a_{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}-a_{12}a_{21}a_{33}-a_{11}a_{23}a_{32}-a_{13}a_{22}a_{31}$
+$=\textcolor{red!70!white}{a_{11}a_{22}a_{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}}\textcolor{blue!70!white}{-a_{12}a_{21}a_{33}-a_{11}a_{23}a_{32}-a_{13}a_{22}a_{31}}$
 \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 $A=B \cdot C \quad \Rightarrow \quad |A|=|B| \cdot |C|$