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

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

$$$\times$$$
$$$\times$$$

Se a calculadora não calculou algo ou você identificou um erro, ou tem uma sugestão/comentário, escreva nos comentários abaixo.

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

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

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