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

A calculadora multiplicará a matriz $$$2$$$ x $$$2$$$ $$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]$$$ pela matriz $$$2$$$ x $$$2$$$ $$$\left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right]$$$, com as etapas mostradas.

Calculadora relacionada: Calculadora matricial

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Sua entrada

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

Solução

$$$\left[\begin{array}{cc}{\color{Crimson}5 e} & {\color{Chocolate}\frac{2}{e^{2}}}\\{\color{Blue}e} & {\color{Fuchsia}e^{-2}}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{OrangeRed}\frac{1}{3}} & {\color{Brown}- \frac{2}{3}}\\{\color{Green}- \frac{1}{3}} & {\color{Blue}\frac{5}{3}}\end{array}\right] = \left[\begin{array}{cc}{\color{Crimson}\left(5 e\right)}\cdot {\color{OrangeRed}\left(\frac{1}{3}\right)} + {\color{Chocolate}\left(\frac{2}{e^{2}}\right)}\cdot {\color{Green}\left(- \frac{1}{3}\right)} & {\color{Crimson}\left(5 e\right)}\cdot {\color{Brown}\left(- \frac{2}{3}\right)} + {\color{Chocolate}\left(\frac{2}{e^{2}}\right)}\cdot {\color{Blue}\left(\frac{5}{3}\right)}\\{\color{Blue}\left(e\right)}\cdot {\color{OrangeRed}\left(\frac{1}{3}\right)} + {\color{Fuchsia}\left(e^{-2}\right)}\cdot {\color{Green}\left(- \frac{1}{3}\right)} & {\color{Blue}\left(e\right)}\cdot {\color{Brown}\left(- \frac{2}{3}\right)} + {\color{Fuchsia}\left(e^{-2}\right)}\cdot {\color{Blue}\left(\frac{5}{3}\right)}\end{array}\right] = \left[\begin{array}{cc}\frac{-2 + 5 e^{3}}{3 e^{2}} & \frac{10 - 10 e^{3}}{3 e^{2}}\\\frac{-1 + e^{3}}{3 e^{2}} & \frac{5 - 2 e^{3}}{3 e^{2}}\end{array}\right]$$$

Responder

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