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矩陣計算器

逐步求解矩陣

此計算器可對兩個矩陣進行加、減、乘、除運算，並可對矩陣求冪，且會顯示步驟。它還能求行列式、逆矩陣、rref（簡化行階梯形）、零空間、秩、特徵值與特徵向量，並可將矩陣乘以純量。

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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 $$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 0 & 4\\0 & 1 & 0\end{array}\right] + \left[\begin{array}{ccc}2 & 1 & 4\\5 & 7 & 1\\1 & 2 & 5\end{array}\right]$$$。

解答

$$$\left[\begin{array}{ccc}{\color{DarkMagenta}1} & {\color{Brown}0} & {\color{Violet}0}\\{\color{Green}0} & {\color{Crimson}0} & {\color{Peru}4}\\{\color{SaddleBrown}0} & {\color{Chocolate}1} & {\color{OrangeRed}0}\end{array}\right] + \left[\begin{array}{ccc}{\color{DarkMagenta}2} & {\color{Brown}1} & {\color{Violet}4}\\{\color{Green}5} & {\color{Crimson}7} & {\color{Peru}1}\\{\color{SaddleBrown}1} & {\color{Chocolate}2} & {\color{OrangeRed}5}\end{array}\right] = \left[\begin{array}{ccc}{\color{DarkMagenta}\left(1\right)} + {\color{DarkMagenta}\left(2\right)} & {\color{Brown}\left(0\right)} + {\color{Brown}\left(1\right)} & {\color{Violet}\left(0\right)} + {\color{Violet}\left(4\right)}\\{\color{Green}\left(0\right)} + {\color{Green}\left(5\right)} & {\color{Crimson}\left(0\right)} + {\color{Crimson}\left(7\right)} & {\color{Peru}\left(4\right)} + {\color{Peru}\left(1\right)}\\{\color{SaddleBrown}\left(0\right)} + {\color{SaddleBrown}\left(1\right)} & {\color{Chocolate}\left(1\right)} + {\color{Chocolate}\left(2\right)} & {\color{OrangeRed}\left(0\right)} + {\color{OrangeRed}\left(5\right)}\end{array}\right] = \left[\begin{array}{ccc}3 & 1 & 4\\5 & 7 & 5\\1 & 3 & 5\end{array}\right]$$$

答案

$$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 0 & 4\\0 & 1 & 0\end{array}\right] + \left[\begin{array}{ccc}2 & 1 & 4\\5 & 7 & 1\\1 & 2 & 5\end{array}\right] = \left[\begin{array}{ccc}3 & 1 & 4\\5 & 7 & 5\\1 & 3 & 5\end{array}\right]$$$A