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矩阵乘法计算器

逐步计算矩阵乘法

该计算器将求两个矩阵的乘积（如果可能），并显示计算步骤。它可对大小不超过 10x10 的矩阵进行相乘（如 2x2、3x3、4x4 等）。

相关计算器: 矩阵计算器

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您的输入

计算 $$$\left[\begin{array}{ccc}4 & 5 & 7\\2 & 1 & 0\end{array}\right]\cdot \left[\begin{array}{cc}2 & 3\\8 & 9\\1 & 1\end{array}\right]$$$。

解答

$$$\left[\begin{array}{ccc}{\color{Crimson}4} & {\color{Green}5} & {\color{Chartreuse}7}\\{\color{Brown}2} & {\color{DarkMagenta}1} & {\color{Purple}0}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{Brown}2} & {\color{BlueViolet}3}\\{\color{DeepPink}8} & {\color{GoldenRod}9}\\{\color{SaddleBrown}1} & {\color{Green}1}\end{array}\right] = \left[\begin{array}{cc}{\color{Crimson}\left(4\right)}\cdot {\color{Brown}\left(2\right)} + {\color{Green}\left(5\right)}\cdot {\color{DeepPink}\left(8\right)} + {\color{Chartreuse}\left(7\right)}\cdot {\color{SaddleBrown}\left(1\right)} & {\color{Crimson}\left(4\right)}\cdot {\color{BlueViolet}\left(3\right)} + {\color{Green}\left(5\right)}\cdot {\color{GoldenRod}\left(9\right)} + {\color{Chartreuse}\left(7\right)}\cdot {\color{Green}\left(1\right)}\\{\color{Brown}\left(2\right)}\cdot {\color{Brown}\left(2\right)} + {\color{DarkMagenta}\left(1\right)}\cdot {\color{DeepPink}\left(8\right)} + {\color{Purple}\left(0\right)}\cdot {\color{SaddleBrown}\left(1\right)} & {\color{Brown}\left(2\right)}\cdot {\color{BlueViolet}\left(3\right)} + {\color{DarkMagenta}\left(1\right)}\cdot {\color{GoldenRod}\left(9\right)} + {\color{Purple}\left(0\right)}\cdot {\color{Green}\left(1\right)}\end{array}\right] = \left[\begin{array}{cc}55 & 64\\12 & 15\end{array}\right]$$$

答案

$$$\left[\begin{array}{ccc}4 & 5 & 7\\2 & 1 & 0\end{array}\right]\cdot \left[\begin{array}{cc}2 & 3\\8 & 9\\1 & 1\end{array}\right] = \left[\begin{array}{cc}55 & 64\\12 & 15\end{array}\right]$$$A