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

계산기는 $$$3$$$x$$$3$$$ 행렬 $$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]$$$$$$3$$$x$$$3$$$ 행렬 $$$\left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$를 곱하며, 단계별 풀이를 보여 줍니다.

관련 계산기: 행렬 계산기

$$$\times$$$
A
$$$\times$$$
A

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

사용자 입력

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

풀이

$$$\left[\begin{array}{ccc}{\color{DarkCyan}0} & {\color{GoldenRod}1} & {\color{Chocolate}1}\\{\color{BlueViolet}\sqrt{2}} & {\color{Chartreuse}2} & {\color{Brown}0}\\{\color{SaddleBrown}0} & {\color{DarkBlue}1} & {\color{DarkMagenta}1}\end{array}\right]\cdot \left[\begin{array}{ccc}{\color{Green}0} & {\color{DarkCyan}\sqrt{2}} & {\color{Chartreuse}0}\\{\color{Violet}1} & {\color{DeepPink}2} & {\color{Crimson}1}\\{\color{Brown}1} & {\color{Blue}0} & {\color{Fuchsia}1}\end{array}\right] = \left[\begin{array}{ccc}{\color{DarkCyan}\left(0\right)}\cdot {\color{Green}\left(0\right)} + {\color{GoldenRod}\left(1\right)}\cdot {\color{Violet}\left(1\right)} + {\color{Chocolate}\left(1\right)}\cdot {\color{Brown}\left(1\right)} & {\color{DarkCyan}\left(0\right)}\cdot {\color{DarkCyan}\left(\sqrt{2}\right)} + {\color{GoldenRod}\left(1\right)}\cdot {\color{DeepPink}\left(2\right)} + {\color{Chocolate}\left(1\right)}\cdot {\color{Blue}\left(0\right)} & {\color{DarkCyan}\left(0\right)}\cdot {\color{Chartreuse}\left(0\right)} + {\color{GoldenRod}\left(1\right)}\cdot {\color{Crimson}\left(1\right)} + {\color{Chocolate}\left(1\right)}\cdot {\color{Fuchsia}\left(1\right)}\\{\color{BlueViolet}\left(\sqrt{2}\right)}\cdot {\color{Green}\left(0\right)} + {\color{Chartreuse}\left(2\right)}\cdot {\color{Violet}\left(1\right)} + {\color{Brown}\left(0\right)}\cdot {\color{Brown}\left(1\right)} & {\color{BlueViolet}\left(\sqrt{2}\right)}\cdot {\color{DarkCyan}\left(\sqrt{2}\right)} + {\color{Chartreuse}\left(2\right)}\cdot {\color{DeepPink}\left(2\right)} + {\color{Brown}\left(0\right)}\cdot {\color{Blue}\left(0\right)} & {\color{BlueViolet}\left(\sqrt{2}\right)}\cdot {\color{Chartreuse}\left(0\right)} + {\color{Chartreuse}\left(2\right)}\cdot {\color{Crimson}\left(1\right)} + {\color{Brown}\left(0\right)}\cdot {\color{Fuchsia}\left(1\right)}\\{\color{SaddleBrown}\left(0\right)}\cdot {\color{Green}\left(0\right)} + {\color{DarkBlue}\left(1\right)}\cdot {\color{Violet}\left(1\right)} + {\color{DarkMagenta}\left(1\right)}\cdot {\color{Brown}\left(1\right)} & {\color{SaddleBrown}\left(0\right)}\cdot {\color{DarkCyan}\left(\sqrt{2}\right)} + {\color{DarkBlue}\left(1\right)}\cdot {\color{DeepPink}\left(2\right)} + {\color{DarkMagenta}\left(1\right)}\cdot {\color{Blue}\left(0\right)} & {\color{SaddleBrown}\left(0\right)}\cdot {\color{Chartreuse}\left(0\right)} + {\color{DarkBlue}\left(1\right)}\cdot {\color{Crimson}\left(1\right)} + {\color{DarkMagenta}\left(1\right)}\cdot {\color{Fuchsia}\left(1\right)}\end{array}\right] = \left[\begin{array}{ccc}2 & 2 & 2\\2 & 6 & 2\\2 & 2 & 2\end{array}\right]$$$

정답

$$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}2 & 2 & 2\\2 & 6 & 2\\2 & 2 & 2\end{array}\right]$$$A