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

La calcolatrice moltiplicherà la matrice $$$\left[\begin{array}{ccc}0 & 1 & 0\\\frac{\sqrt{2}}{2} & \sqrt{2} & \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2}\end{array}\right]$$$ di dimensioni $$$3$$$x$$$3$$$ per la matrice $$$\left[\begin{array}{c}\frac{\sqrt{3}}{3}\\- \frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\end{array}\right]$$$ di dimensioni $$$3$$$x$$$1$$$, mostrando i passaggi.

Calcolatore correlato: Calcolatrice di matrici

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Il tuo input

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

Soluzione

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

Risposta

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