$$$\left[\begin{array}{ccc}0 & 1 & 0\\\frac{\sqrt{2}}{2} & \sqrt{2} & \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{3}}{3}\\- \frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\end{array}\right]$$$

Berechne $$$\left[\begin{array}{ccc}0 & 1 & 0\\\frac{\sqrt{2}}{2} & \sqrt{2} & \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{3}}{3}\\- \frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\end{array}\right].$$$

$$$\left[\begin{array}{ccc}{\color{Purple}0} & {\color{BlueViolet}1} & {\color{Peru}0}\\{\color{Magenta}\frac{\sqrt{2}}{2}} & {\color{DarkBlue}\sqrt{2}} & {\color{DeepPink}\frac{\sqrt{2}}{2}}\\{\color{Fuchsia}\frac{\sqrt{2}}{2}} & {\color{SaddleBrown}0} & {\color{Brown}\frac{\sqrt{2}}{2}}\end{array}\right]\cdot \left[\begin{array}{c}{\color{OrangeRed}\frac{\sqrt{3}}{3}}\\{\color{Violet}- \frac{\sqrt{3}}{3}}\\{\color{Chocolate}\frac{\sqrt{3}}{3}}\end{array}\right] = \left[\begin{array}{c}{\color{Purple}\left(0\right)}\cdot {\color{OrangeRed}\left(\frac{\sqrt{3}}{3}\right)} + {\color{BlueViolet}\left(1\right)}\cdot {\color{Violet}\left(- \frac{\sqrt{3}}{3}\right)} + {\color{Peru}\left(0\right)}\cdot {\color{Chocolate}\left(\frac{\sqrt{3}}{3}\right)}\\{\color{Magenta}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{OrangeRed}\left(\frac{\sqrt{3}}{3}\right)} + {\color{DarkBlue}\left(\sqrt{2}\right)}\cdot {\color{Violet}\left(- \frac{\sqrt{3}}{3}\right)} + {\color{DeepPink}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Chocolate}\left(\frac{\sqrt{3}}{3}\right)}\\{\color{Fuchsia}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{OrangeRed}\left(\frac{\sqrt{3}}{3}\right)} + {\color{SaddleBrown}\left(0\right)}\cdot {\color{Violet}\left(- \frac{\sqrt{3}}{3}\right)} + {\color{Brown}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Chocolate}\left(\frac{\sqrt{3}}{3}\right)}\end{array}\right] = \left[\begin{array}{c}- \frac{\sqrt{3}}{3}\\0\\\frac{\sqrt{6}}{3}\end{array}\right]$$$

$$$\left[\begin{array}{ccc}0 & 1 & 0\\\frac{\sqrt{2}}{2} & \sqrt{2} & \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{3}}{3}\\- \frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\end{array}\right] = \left[\begin{array}{c}- \frac{\sqrt{3}}{3}\\0\\\frac{\sqrt{6}}{3}\end{array}\right]\approx \left[\begin{array}{c}-0.577350269189626\\0\\0.816496580927726\end{array}\right]$$$A