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

이 계산기는 $$$3$$$x$$$3$$$ 행렬 $$$\left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$에 스칼라 $$$\frac{\sqrt{2}}{4}$$$를 곱하며, 단계별 과정을 보여줍니다.

행렬의 크기:

$$$\times$$$

행렬:

스칼라:

계산기가 예상대로 작동하지 않았거나 오류를 신고하거나 피드백을 공유하고 싶으시다면 문의해 주세요.

사용자 입력

$$$\frac{\sqrt{2}}{4} \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$을(를) 계산하세요.

풀이

행렬의 각 성분에 스칼라를 곱하시오:

$$${\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}{\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(0\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(\sqrt{2}\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(0\right)\\{\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(1\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(2\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(1\right)\\{\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(1\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(0\right) & {\color{DeepPink}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(1\right)\end{array}\right] = \left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]$$$

정답

$$$\frac{\sqrt{2}}{4} \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\approx \left[\begin{array}{ccc}0 & 0.5 & 0\\0.353553390593274 & 0.707106781186548 & 0.353553390593274\\0.353553390593274 & 0 & 0.353553390593274\end{array}\right]$$$A