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

The calculator will multiply the $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]$$$ by the $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right]$$$, with steps shown.

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Your Input

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

Solution

$$$\left[\begin{array}{cc}{\color{Violet}5 e} & {\color{Peru}\frac{2}{e^{2}}}\\{\color{Chartreuse}e} & {\color{Green}e^{-2}}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{GoldenRod}\frac{1}{3}} & {\color{BlueViolet}- \frac{2}{3}}\\{\color{Chartreuse}- \frac{1}{3}} & {\color{Chocolate}\frac{5}{3}}\end{array}\right] = \left[\begin{array}{cc}{\color{Violet}\left(5 e\right)}\cdot {\color{GoldenRod}\left(\frac{1}{3}\right)} + {\color{Peru}\left(\frac{2}{e^{2}}\right)}\cdot {\color{Chartreuse}\left(- \frac{1}{3}\right)} & {\color{Violet}\left(5 e\right)}\cdot {\color{BlueViolet}\left(- \frac{2}{3}\right)} + {\color{Peru}\left(\frac{2}{e^{2}}\right)}\cdot {\color{Chocolate}\left(\frac{5}{3}\right)}\\{\color{Chartreuse}\left(e\right)}\cdot {\color{GoldenRod}\left(\frac{1}{3}\right)} + {\color{Green}\left(e^{-2}\right)}\cdot {\color{Chartreuse}\left(- \frac{1}{3}\right)} & {\color{Chartreuse}\left(e\right)}\cdot {\color{BlueViolet}\left(- \frac{2}{3}\right)} + {\color{Green}\left(e^{-2}\right)}\cdot {\color{Chocolate}\left(\frac{5}{3}\right)}\end{array}\right] = \left[\begin{array}{cc}\frac{-2 + 5 e^{3}}{3 e^{2}} & \frac{10 - 10 e^{3}}{3 e^{2}}\\\frac{-1 + e^{3}}{3 e^{2}} & \frac{5 - 2 e^{3}}{3 e^{2}}\end{array}\right]$$$

Answer

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