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$$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$

La calculatrice multipliera la matrice $$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]$$$ de dimension $$$3$$$x$$$3$$$ par la matrice $$$\left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$ de dimension $$$3$$$x$$$3$$$, en montrant les étapes.

Calculatrice associée: Calculatrice de matrices

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Votre saisie

Calculer $$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right].$$$

Solution

$$$\left[\begin{array}{ccc}{\color{Purple}0} & {\color{SaddleBrown}1} & {\color{BlueViolet}1}\\{\color{Crimson}\sqrt{2}} & {\color{Peru}2} & {\color{Fuchsia}0}\\{\color{Brown}0} & {\color{Violet}1} & {\color{DarkBlue}1}\end{array}\right]\cdot \left[\begin{array}{ccc}{\color{Crimson}0} & {\color{Green}\sqrt{2}} & {\color{Chartreuse}0}\\{\color{Purple}1} & {\color{Red}2} & {\color{BlueViolet}1}\\{\color{DarkMagenta}1} & {\color{Peru}0} & {\color{Violet}1}\end{array}\right] = \left[\begin{array}{ccc}{\color{Purple}\left(0\right)}\cdot {\color{Crimson}\left(0\right)} + {\color{SaddleBrown}\left(1\right)}\cdot {\color{Purple}\left(1\right)} + {\color{BlueViolet}\left(1\right)}\cdot {\color{DarkMagenta}\left(1\right)} & {\color{Purple}\left(0\right)}\cdot {\color{Green}\left(\sqrt{2}\right)} + {\color{SaddleBrown}\left(1\right)}\cdot {\color{Red}\left(2\right)} + {\color{BlueViolet}\left(1\right)}\cdot {\color{Peru}\left(0\right)} & {\color{Purple}\left(0\right)}\cdot {\color{Chartreuse}\left(0\right)} + {\color{SaddleBrown}\left(1\right)}\cdot {\color{BlueViolet}\left(1\right)} + {\color{BlueViolet}\left(1\right)}\cdot {\color{Violet}\left(1\right)}\\{\color{Crimson}\left(\sqrt{2}\right)}\cdot {\color{Crimson}\left(0\right)} + {\color{Peru}\left(2\right)}\cdot {\color{Purple}\left(1\right)} + {\color{Fuchsia}\left(0\right)}\cdot {\color{DarkMagenta}\left(1\right)} & {\color{Crimson}\left(\sqrt{2}\right)}\cdot {\color{Green}\left(\sqrt{2}\right)} + {\color{Peru}\left(2\right)}\cdot {\color{Red}\left(2\right)} + {\color{Fuchsia}\left(0\right)}\cdot {\color{Peru}\left(0\right)} & {\color{Crimson}\left(\sqrt{2}\right)}\cdot {\color{Chartreuse}\left(0\right)} + {\color{Peru}\left(2\right)}\cdot {\color{BlueViolet}\left(1\right)} + {\color{Fuchsia}\left(0\right)}\cdot {\color{Violet}\left(1\right)}\\{\color{Brown}\left(0\right)}\cdot {\color{Crimson}\left(0\right)} + {\color{Violet}\left(1\right)}\cdot {\color{Purple}\left(1\right)} + {\color{DarkBlue}\left(1\right)}\cdot {\color{DarkMagenta}\left(1\right)} & {\color{Brown}\left(0\right)}\cdot {\color{Green}\left(\sqrt{2}\right)} + {\color{Violet}\left(1\right)}\cdot {\color{Red}\left(2\right)} + {\color{DarkBlue}\left(1\right)}\cdot {\color{Peru}\left(0\right)} & {\color{Brown}\left(0\right)}\cdot {\color{Chartreuse}\left(0\right)} + {\color{Violet}\left(1\right)}\cdot {\color{BlueViolet}\left(1\right)} + {\color{DarkBlue}\left(1\right)}\cdot {\color{Violet}\left(1\right)}\end{array}\right] = \left[\begin{array}{ccc}2 & 2 & 2\\2 & 6 & 2\\2 & 2 & 2\end{array}\right]$$$

Réponse

$$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}2 & 2 & 2\\2 & 6 & 2\\2 & 2 & 2\end{array}\right]$$$A