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$$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]\cdot \left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right]$$$

この計算機は、$$$2$$$x$$$2$$$ 行列 $$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]$$$ に $$$2$$$x$$$2$$$ 行列 $$$\left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right]$$$ を掛け、手順を示しながら計算します。

関連する計算機: 行列計算機

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計算機が期待どおりに動作しなかった場合、またはエラーの報告やフィードバックがある場合は、お問い合わせください。

入力内容

$$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]\cdot \left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right]$$$を計算せよ。

解答

$$$\left[\begin{array}{cc}{\color{Crimson}5 e} & {\color{Brown}\frac{2}{e^{2}}}\\{\color{Purple}e} & {\color{DarkBlue}e^{-2}}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{Chocolate}\frac{1}{3}} & {\color{Purple}- \frac{2}{3}}\\{\color{DeepPink}- \frac{1}{3}} & {\color{Violet}\frac{5}{3}}\end{array}\right] = \left[\begin{array}{cc}{\color{Crimson}\left(5 e\right)}\cdot {\color{Chocolate}\left(\frac{1}{3}\right)} + {\color{Brown}\left(\frac{2}{e^{2}}\right)}\cdot {\color{DeepPink}\left(- \frac{1}{3}\right)} & {\color{Crimson}\left(5 e\right)}\cdot {\color{Purple}\left(- \frac{2}{3}\right)} + {\color{Brown}\left(\frac{2}{e^{2}}\right)}\cdot {\color{Violet}\left(\frac{5}{3}\right)}\\{\color{Purple}\left(e\right)}\cdot {\color{Chocolate}\left(\frac{1}{3}\right)} + {\color{DarkBlue}\left(e^{-2}\right)}\cdot {\color{DeepPink}\left(- \frac{1}{3}\right)} & {\color{Purple}\left(e\right)}\cdot {\color{Purple}\left(- \frac{2}{3}\right)} + {\color{DarkBlue}\left(e^{-2}\right)}\cdot {\color{Violet}\left(\frac{5}{3}\right)}\end{array}\right] = \left[\begin{array}{cc}\frac{-2 + 5 e^{3}}{3 e^{2}} & \frac{10 - 10 e^{3}}{3 e^{2}}\\\frac{-1 + e^{3}}{3 e^{2}} & \frac{5 - 2 e^{3}}{3 e^{2}}\end{array}\right]$$$

解答

$$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]\cdot \left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right] = \left[\begin{array}{cc}\frac{-2 + 5 e^{3}}{3 e^{2}} & \frac{10 - 10 e^{3}}{3 e^{2}}\\\frac{-1 + e^{3}}{3 e^{2}} & \frac{5 - 2 e^{3}}{3 e^{2}}\end{array}\right]\approx \left[\begin{array}{cc}4.440246191940667 & -8.609821817408108\\0.860982181740811 & -1.586629080245009\end{array}\right]$$$A