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$$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right]$$$

A calculadora multiplicará a matriz $$$3$$$ x $$$3$$$ $$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]$$$ pela matriz $$$3$$$ x $$$1$$$ $$$\left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right]$$$, com as etapas mostradas.

Calculadora relacionada: Calculadora matricial

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Sua entrada

Calcule $$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right].$$$

Solução

$$$\left[\begin{array}{ccc}{\color{Green}0} & {\color{Fuchsia}\frac{1}{2}} & {\color{DarkBlue}0}\\{\color{BlueViolet}\frac{\sqrt{2}}{4}} & {\color{Red}\frac{\sqrt{2}}{2}} & {\color{Brown}\frac{\sqrt{2}}{4}}\\{\color{Magenta}\frac{\sqrt{2}}{4}} & {\color{DarkMagenta}0} & {\color{SaddleBrown}\frac{\sqrt{2}}{4}}\end{array}\right]\cdot \left[\begin{array}{c}{\color{DarkCyan}\frac{\sqrt{6}}{6}}\\{\color{DarkBlue}\frac{\sqrt{6}}{3}}\\{\color{Brown}\frac{\sqrt{6}}{6}}\end{array}\right] = \left[\begin{array}{c}{\color{Green}\left(0\right)}\cdot {\color{DarkCyan}\left(\frac{\sqrt{6}}{6}\right)} + {\color{Fuchsia}\left(\frac{1}{2}\right)}\cdot {\color{DarkBlue}\left(\frac{\sqrt{6}}{3}\right)} + {\color{DarkBlue}\left(0\right)}\cdot {\color{Brown}\left(\frac{\sqrt{6}}{6}\right)}\\{\color{BlueViolet}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{DarkCyan}\left(\frac{\sqrt{6}}{6}\right)} + {\color{Red}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{DarkBlue}\left(\frac{\sqrt{6}}{3}\right)} + {\color{Brown}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Brown}\left(\frac{\sqrt{6}}{6}\right)}\\{\color{Magenta}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{DarkCyan}\left(\frac{\sqrt{6}}{6}\right)} + {\color{DarkMagenta}\left(0\right)}\cdot {\color{DarkBlue}\left(\frac{\sqrt{6}}{3}\right)} + {\color{SaddleBrown}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Brown}\left(\frac{\sqrt{6}}{6}\right)}\end{array}\right] = \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{3}}{2}\\\frac{\sqrt{3}}{6}\end{array}\right]$$$

Responder

$$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right] = \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{3}}{2}\\\frac{\sqrt{3}}{6}\end{array}\right]\approx \left[\begin{array}{c}0.408248290463863\\0.866025403784439\\0.288675134594813\end{array}\right]$$$A