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[2222]⋅[2222]\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 11x22 matrix [2222]\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right] by the 22x11 matrix [2222]\left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right], with steps shown.

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Your Input

Calculate [2222]⋅[2222].\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

[2222]⋅[2222]=[(22)⋅(22)+(22)⋅(22)]=[1]\left[\begin{array}{cc}{\color{GoldenRod}\frac{\sqrt{2}}{2}} & {\color{BlueViolet}\frac{\sqrt{2}}{2}}\end{array}\right]\cdot \left[\begin{array}{c}{\color{DarkBlue}\frac{\sqrt{2}}{2}}\\{\color{OrangeRed}\frac{\sqrt{2}}{2}}\end{array}\right] = \left[\begin{array}{c}{\color{GoldenRod}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{DarkBlue}\left(\frac{\sqrt{2}}{2}\right)} + {\color{BlueViolet}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{OrangeRed}\left(\frac{\sqrt{2}}{2}\right)}\end{array}\right] = \left[\begin{array}{c}1\end{array}\right]

Answer

[2222]⋅[2222]=[1]\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