diff --git a/exercise1/Theorie.pdf b/exercise1/Theorie.pdf
index 704cd80..eb21719 100644
Binary files a/exercise1/Theorie.pdf and b/exercise1/Theorie.pdf differ
diff --git a/exercise1/Theorie.tex b/exercise1/Theorie.tex
index 01d1f5d..8096b96 100644
--- a/exercise1/Theorie.tex
+++ b/exercise1/Theorie.tex
@@ -106,12 +106,12 @@ $\Rightarrow S \times T \neq T \times S \Rightarrow$ does not commute\\
 \subsection*{1.1.2}
 \subsection*{a)}
 \begin{gather*}
-\begin{pmatrix} 1 & 0 & 0  \\ 0&1&0\\ 0&0&1 \\ \end{pmatrix} \times \begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ y_1&y_2&\cdots&y_n\\ z_1&z_2&\cdots&z_n \\ \end{pmatrix} =\begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ z_1&z_2&\cdots&z_n\\ y_1&y_2&\cdots&y_n \\ \end{pmatrix}
+\begin{pmatrix} 1 & 0 & 0  \\ 0&0&1\\ 0&1&0 \\ \end{pmatrix} \times \begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ y_1&y_2&\cdots&y_n\\ z_1&z_2&\cdots&z_n \\ \end{pmatrix} =\begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ z_1&z_2&\cdots&z_n\\ y_1&y_2&\cdots&y_n \\ \end{pmatrix}
 \end{gather*}
 
 \subsection*{b)}
 \begin{gather*}
-\begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ y_1&y_2&\cdots&y_n\\ z_1&z_2&\cdots&z_n \\ \end{pmatrix} \times n \downarrow \begin{pmatrix} 1 \\ 1 \\ \vdots \\ 1 \\ \end{pmatrix} = 
+\begin{pmatrix} x_1 & x_2 & \cdots & x_n \\ y_1&y_2&\cdots&y_n\\ z_1&z_2&\cdots&z_n \\ \end{pmatrix} \times \begin{pmatrix} 1 \\ 1 \\ \vdots \\ 1 \\ \end{pmatrix} = 
 \begin{pmatrix}  \sum\limits_{i=1} x_i \\ \sum\limits_{i=1} y_i \\ \sum\limits_{i=1} z_i \end{pmatrix}
 \end{gather*}