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

该计算器将把$$$1$$$x$$$2$$$矩阵$$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]$$$与$$$2$$$x$$$1$$$矩阵$$$\left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right]$$$相乘，并显示计算步骤。

您的输入

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

解答

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

答案

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