Addiere den Vektor $\overset\rightharpoonup v$ zu dem Ortsvektor $\overset\rightharpoonup P$

$\color{orange}{\overset\rightharpoonup{P'}}=\color{purple}{\overset\rightharpoonup{P}} + \color{red}{\overset\rightharpoonup v} =\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}1\\-3\end{pmatrix}$

$x_{P'}=-2+1=-1$

$y_{P'}=1+(-3)=-2$

$\rightarrow\color{orange}{P'(-1|-2)}$

$\textcolor{orange}{\overset\rightharpoonup{P'}}=\begin{pmatrix}1&0\\0&1\end{pmatrix}\cdot\textcolor{purple}{\overset\rightharpoonup P} +\textcolor{red}{\overset\rightharpoonup v}=\begin{pmatrix}1&0\\0&1\end{pmatrix}\cdot\textcolor{purple}{\begin{pmatrix}-2\\1\end{pmatrix}}+\textcolor{red}{\begin{pmatrix}1\\-3\end{pmatrix}}$

Führe die Matrix-Vektor-Multiplikation durch.

$\begin{pmatrix}1&0\\0&1\end{pmatrix}\cdot\begin{pmatrix}-2\\1\end{pmatrix}=\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}1\\-3\end{pmatrix}$

Addiere die Vektoren

$\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}1\\-3\end{pmatrix}=\begin{pmatrix}-1\\-2\end{pmatrix}$

$\rightarrow \color{orange}{\overset\rightharpoonup {P'}}=\color{orange}{\begin{pmatrix}-1\\-2\end{pmatrix}}$

$\textcolor{orange}{\overset\rightharpoonup{P'}}=\textcolor{purple}{\overset\rightharpoonup{P}}+\textcolor{red}{\overset\rightharpoonup{v}}=\textcolor{purple}{\begin{pmatrix}-3{,}2\\2{,}4\end{pmatrix}}+\textcolor{red}{\begin{pmatrix}1{,}4\\-1{,}7\end{pmatrix}}$

$x_{P'}=-3{,}2+1{,}4=-1{,}8$

$y_{P'}=2{,}4+(-1{,}7)=0{,}7$

$\rightarrow \color{orange}{P'(-1{,}8|0{,}7)}$

$\color{orange}{\overset\rightharpoonup{P'}}=\begin{pmatrix}1&0\\0&1\end{pmatrix}\cdot\color{purple}{\overset\rightharpoonup{P}}+\color{red}{\overset\rightharpoonup{v}}=\begin{pmatrix}1&0\\0&1\end{pmatrix}\cdot\color{purple}{\begin{pmatrix}-3{,}2\\2{,}4\end{pmatrix}}+\color{red}{\begin{pmatrix}1{,}4\\-1{,}7\end{pmatrix}}$

Führe die Matrix-Vektor-Multiplikation durch

$\begin{pmatrix}1&0\\0&1\end{pmatrix}\cdot\color{purple}{\begin{pmatrix}-3{,}2\\2{,}4\end{pmatrix}}+\begin{pmatrix}1{,}4\\-1{,}7\end{pmatrix}=\begin{pmatrix}-3{,}2\\2{,}4\end{pmatrix}+\begin{pmatrix}1{,}4\\-1{,}7\end{pmatrix}$

Addiere die Vektoren

$\begin{pmatrix}-3{,}2\\2{,}4\end{pmatrix}+\begin{pmatrix}1{,}4\\-1{,}7\end{pmatrix}=\begin{pmatrix}-1{,}8\\0{,}7\end{pmatrix}$

$\rightarrow \color{orange}{\overset\rightharpoonup {P'}}=\color{orange}{\begin{pmatrix}-1{,}8\\0{,}7\end{pmatrix}}$