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$$$\frac{\sqrt{2}}{2} \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$
Ihre Eingabe
Berechne $$$\frac{\sqrt{2}}{2} \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$.
Lösung
Multiplizieren Sie jeden Eintrag der Matrix mit dem Skalar:
$$${\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}{\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(0\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(\sqrt{2}\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(0\right)\\{\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(1\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(2\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(1\right)\\{\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(1\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(0\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(1\right)\end{array}\right] = \left[\begin{array}{ccc}0 & 1 & 0\\\frac{\sqrt{2}}{2} & \sqrt{2} & \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2}\end{array}\right]$$$
Antwort
$$$\frac{\sqrt{2}}{2} \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}0 & 1 & 0\\\frac{\sqrt{2}}{2} & \sqrt{2} & \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2}\end{array}\right]\approx \left[\begin{array}{ccc}0 & 1 & 0\\0.707106781186548 & 1.414213562373095 & 0.707106781186548\\0.707106781186548 & 0 & 0.707106781186548\end{array}\right]$$$A