$$$\frac{\sqrt{2}}{4} \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$
入力内容
$$$\frac{\sqrt{2}}{4} \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$を計算せよ。
解答
行列の各成分にスカラーを掛けよ:
$$${\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}{\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(0\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(\sqrt{2}\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(0\right)\\{\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(1\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(2\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(1\right)\\{\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(1\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(0\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(1\right)\end{array}\right] = \left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]$$$
解答
$$$\frac{\sqrt{2}}{4} \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\approx \left[\begin{array}{ccc}0 & 0.5 & 0\\0.353553390593274 & 0.707106781186548 & 0.353553390593274\\0.353553390593274 & 0 & 0.353553390593274\end{array}\right]$$$A