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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 calculatrice multipliera la matrice $$$\left[\begin{array}{ccc}0 & 1 & 0\\\frac{\sqrt{2}}{2} & \sqrt{2} & \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2}\end{array}\right]$$$ de dimension $$$3$$$x$$$3$$$ par la matrice $$$\left[\begin{array}{c}\frac{\sqrt{3}}{3}\\- \frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\end{array}\right]$$$ de dimension $$$3$$$x$$$1$$$, en montrant les étapes.

Calculatrice associée: Calculatrice de matrices

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Votre saisie

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

Solution

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

Réponse

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