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$$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right]$$$

The calculator will multiply the $$$1$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]$$$ by the $$$2$$$x$$$1$$$ matrix $$$\left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right]$$$, with steps shown.

Related calculator: Matrix Calculator

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Your Input

Calculate $$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right].$$$

Solution

$$$\left[\begin{array}{cc}{\color{Green}\frac{\sqrt{2}}{2}} & {\color{Purple}\frac{\sqrt{2}}{2}}\end{array}\right]\cdot \left[\begin{array}{c}{\color{Purple}\frac{\sqrt{2}}{2}}\\{\color{BlueViolet}\frac{\sqrt{2}}{2}}\end{array}\right] = \left[\begin{array}{c}{\color{Green}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Purple}\left(\frac{\sqrt{2}}{2}\right)} + {\color{Purple}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{BlueViolet}\left(\frac{\sqrt{2}}{2}\right)}\end{array}\right] = \left[\begin{array}{c}1\end{array}\right]$$$

Answer

$$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right] = \left[\begin{array}{c}1\end{array}\right]$$$A


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