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exc 1 theorie finale adjust

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fruitstaa 2018-11-12 11:42:52 +01:00
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commit 8513cfb34e
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exercise1/Theorie.pdf
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exercise1/Theorie.tex
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@ -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*}