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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 calculadora multiplicará la matriz $$$3$$$ x $$$3$$$ $$$\left[\begin{array}{ccc}0 & 1 & 0\\\frac{\sqrt{2}}{2} & \sqrt{2} & \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2}\end{array}\right]$$$ por la matriz $$$3$$$ x $$$1$$$ $$$\left[\begin{array}{c}\frac{\sqrt{3}}{3}\\- \frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\end{array}\right]$$$, y se muestran los pasos.

Calculadora relacionada: Calculadora de matrices

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Si la calculadora no calculó algo o ha identificado un error, o tiene una sugerencia/comentario, escríbalo en los comentarios a continuación.

Tu aportación

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

Solución

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

Respuesta

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