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

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

Calculadora relacionada: Calculadora matricial

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Sua entrada

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

Solução

$$$\left[\begin{array}{ccc}{\color{OrangeRed}0} & {\color{Chocolate}1} & {\color{Purple}0}\\{\color{Crimson}\frac{\sqrt{2}}{2}} & {\color{Chartreuse}\sqrt{2}} & {\color{Magenta}\frac{\sqrt{2}}{2}}\\{\color{Red}\frac{\sqrt{2}}{2}} & {\color{GoldenRod}0} & {\color{Peru}\frac{\sqrt{2}}{2}}\end{array}\right]\cdot \left[\begin{array}{c}{\color{Fuchsia}\frac{\sqrt{3}}{3}}\\{\color{DarkCyan}- \frac{\sqrt{3}}{3}}\\{\color{Purple}\frac{\sqrt{3}}{3}}\end{array}\right] = \left[\begin{array}{c}{\color{OrangeRed}\left(0\right)}\cdot {\color{Fuchsia}\left(\frac{\sqrt{3}}{3}\right)} + {\color{Chocolate}\left(1\right)}\cdot {\color{DarkCyan}\left(- \frac{\sqrt{3}}{3}\right)} + {\color{Purple}\left(0\right)}\cdot {\color{Purple}\left(\frac{\sqrt{3}}{3}\right)}\\{\color{Crimson}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Fuchsia}\left(\frac{\sqrt{3}}{3}\right)} + {\color{Chartreuse}\left(\sqrt{2}\right)}\cdot {\color{DarkCyan}\left(- \frac{\sqrt{3}}{3}\right)} + {\color{Magenta}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Purple}\left(\frac{\sqrt{3}}{3}\right)}\\{\color{Red}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Fuchsia}\left(\frac{\sqrt{3}}{3}\right)} + {\color{GoldenRod}\left(0\right)}\cdot {\color{DarkCyan}\left(- \frac{\sqrt{3}}{3}\right)} + {\color{Peru}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Purple}\left(\frac{\sqrt{3}}{3}\right)}\end{array}\right] = \left[\begin{array}{c}- \frac{\sqrt{3}}{3}\\0\\\frac{\sqrt{6}}{3}\end{array}\right]$$$

Responder

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