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

La calculadora multiplicará la matriz $$$3$$$ x $$$3$$$ $$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]$$$ por la matriz $$$3$$$ x $$$1$$$ $$$\left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right]$$$, 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 $$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right].$$$

Solución

$$$\left[\begin{array}{ccc}{\color{DarkCyan}0} & {\color{Green}\frac{1}{2}} & {\color{Crimson}0}\\{\color{GoldenRod}\frac{\sqrt{2}}{4}} & {\color{Purple}\frac{\sqrt{2}}{2}} & {\color{Violet}\frac{\sqrt{2}}{4}}\\{\color{Peru}\frac{\sqrt{2}}{4}} & {\color{DeepPink}0} & {\color{Brown}\frac{\sqrt{2}}{4}}\end{array}\right]\cdot \left[\begin{array}{c}{\color{Purple}\frac{\sqrt{6}}{6}}\\{\color{Brown}\frac{\sqrt{6}}{3}}\\{\color{Fuchsia}\frac{\sqrt{6}}{6}}\end{array}\right] = \left[\begin{array}{c}{\color{DarkCyan}\left(0\right)}\cdot {\color{Purple}\left(\frac{\sqrt{6}}{6}\right)} + {\color{Green}\left(\frac{1}{2}\right)}\cdot {\color{Brown}\left(\frac{\sqrt{6}}{3}\right)} + {\color{Crimson}\left(0\right)}\cdot {\color{Fuchsia}\left(\frac{\sqrt{6}}{6}\right)}\\{\color{GoldenRod}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Purple}\left(\frac{\sqrt{6}}{6}\right)} + {\color{Purple}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Brown}\left(\frac{\sqrt{6}}{3}\right)} + {\color{Violet}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Fuchsia}\left(\frac{\sqrt{6}}{6}\right)}\\{\color{Peru}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Purple}\left(\frac{\sqrt{6}}{6}\right)} + {\color{DeepPink}\left(0\right)}\cdot {\color{Brown}\left(\frac{\sqrt{6}}{3}\right)} + {\color{Brown}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Fuchsia}\left(\frac{\sqrt{6}}{6}\right)}\end{array}\right] = \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{3}}{2}\\\frac{\sqrt{3}}{6}\end{array}\right]$$$

Respuesta

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