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矩陣乘法計算器

逐步計算矩陣乘積

此計算器將在可行時求出兩個矩陣的乘積，並顯示計算步驟。它可相乘任意大小的矩陣，最大至 10x10 (2x2, 3x3, 4x4 等)。

相關計算器: 矩陣計算器

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如果計算器未能計算某些內容，或您發現了錯誤，或您有任何建議／回饋，請聯絡我們。

您的輸入

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

解答

$$$\left[\begin{array}{ccc}{\color{BlueViolet}4} & {\color{OrangeRed}5} & {\color{DeepPink}7}\\{\color{Fuchsia}2} & {\color{Violet}1} & {\color{SaddleBrown}0}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{Peru}2} & {\color{Chocolate}3}\\{\color{Red}8} & {\color{Blue}9}\\{\color{BlueViolet}1} & {\color{Chartreuse}1}\end{array}\right] = \left[\begin{array}{cc}{\color{BlueViolet}\left(4\right)}\cdot {\color{Peru}\left(2\right)} + {\color{OrangeRed}\left(5\right)}\cdot {\color{Red}\left(8\right)} + {\color{DeepPink}\left(7\right)}\cdot {\color{BlueViolet}\left(1\right)} & {\color{BlueViolet}\left(4\right)}\cdot {\color{Chocolate}\left(3\right)} + {\color{OrangeRed}\left(5\right)}\cdot {\color{Blue}\left(9\right)} + {\color{DeepPink}\left(7\right)}\cdot {\color{Chartreuse}\left(1\right)}\\{\color{Fuchsia}\left(2\right)}\cdot {\color{Peru}\left(2\right)} + {\color{Violet}\left(1\right)}\cdot {\color{Red}\left(8\right)} + {\color{SaddleBrown}\left(0\right)}\cdot {\color{BlueViolet}\left(1\right)} & {\color{Fuchsia}\left(2\right)}\cdot {\color{Chocolate}\left(3\right)} + {\color{Violet}\left(1\right)}\cdot {\color{Blue}\left(9\right)} + {\color{SaddleBrown}\left(0\right)}\cdot {\color{Chartreuse}\left(1\right)}\end{array}\right] = \left[\begin{array}{cc}55 & 64\\12 & 15\end{array}\right]$$$

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