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$$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]\cdot \left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]$$$

Der Rechner multipliziert die $$$3$$$x$$$3$$$-Matrix $$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]$$$ mit der $$$3$$$x$$$3$$$-Matrix $$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]$$$ und zeigt dabei die Rechenschritte.

Verwandter Rechner: Matrizenrechner

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Ihre Eingabe

Berechne $$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]\cdot \left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right].$$$

Lösung

$$$\left[\begin{array}{ccc}{\color{DarkBlue}1} & {\color{Purple}3} & {\color{BlueViolet}4}\\{\color{Chartreuse}-1} & {\color{Green}-8} & {\color{Fuchsia}5}\\{\color{Peru}0} & {\color{Magenta}6} & {\color{DarkMagenta}-7}\end{array}\right]\cdot \left[\begin{array}{ccc}{\color{Chocolate}1} & {\color{Brown}3} & {\color{DarkMagenta}4}\\{\color{Purple}-1} & {\color{Blue}-8} & {\color{Peru}5}\\{\color{DeepPink}0} & {\color{DarkBlue}6} & {\color{DarkCyan}-7}\end{array}\right] = \left[\begin{array}{ccc}{\color{DarkBlue}\left(1\right)}\cdot {\color{Chocolate}\left(1\right)} + {\color{Purple}\left(3\right)}\cdot {\color{Purple}\left(-1\right)} + {\color{BlueViolet}\left(4\right)}\cdot {\color{DeepPink}\left(0\right)} & {\color{DarkBlue}\left(1\right)}\cdot {\color{Brown}\left(3\right)} + {\color{Purple}\left(3\right)}\cdot {\color{Blue}\left(-8\right)} + {\color{BlueViolet}\left(4\right)}\cdot {\color{DarkBlue}\left(6\right)} & {\color{DarkBlue}\left(1\right)}\cdot {\color{DarkMagenta}\left(4\right)} + {\color{Purple}\left(3\right)}\cdot {\color{Peru}\left(5\right)} + {\color{BlueViolet}\left(4\right)}\cdot {\color{DarkCyan}\left(-7\right)}\\{\color{Chartreuse}\left(-1\right)}\cdot {\color{Chocolate}\left(1\right)} + {\color{Green}\left(-8\right)}\cdot {\color{Purple}\left(-1\right)} + {\color{Fuchsia}\left(5\right)}\cdot {\color{DeepPink}\left(0\right)} & {\color{Chartreuse}\left(-1\right)}\cdot {\color{Brown}\left(3\right)} + {\color{Green}\left(-8\right)}\cdot {\color{Blue}\left(-8\right)} + {\color{Fuchsia}\left(5\right)}\cdot {\color{DarkBlue}\left(6\right)} & {\color{Chartreuse}\left(-1\right)}\cdot {\color{DarkMagenta}\left(4\right)} + {\color{Green}\left(-8\right)}\cdot {\color{Peru}\left(5\right)} + {\color{Fuchsia}\left(5\right)}\cdot {\color{DarkCyan}\left(-7\right)}\\{\color{Peru}\left(0\right)}\cdot {\color{Chocolate}\left(1\right)} + {\color{Magenta}\left(6\right)}\cdot {\color{Purple}\left(-1\right)} + {\color{DarkMagenta}\left(-7\right)}\cdot {\color{DeepPink}\left(0\right)} & {\color{Peru}\left(0\right)}\cdot {\color{Brown}\left(3\right)} + {\color{Magenta}\left(6\right)}\cdot {\color{Blue}\left(-8\right)} + {\color{DarkMagenta}\left(-7\right)}\cdot {\color{DarkBlue}\left(6\right)} & {\color{Peru}\left(0\right)}\cdot {\color{DarkMagenta}\left(4\right)} + {\color{Magenta}\left(6\right)}\cdot {\color{Peru}\left(5\right)} + {\color{DarkMagenta}\left(-7\right)}\cdot {\color{DarkCyan}\left(-7\right)}\end{array}\right] = \left[\begin{array}{ccc}-2 & 3 & -9\\7 & 91 & -79\\-6 & -90 & 79\end{array}\right]$$$

Antwort

$$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]\cdot \left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right] = \left[\begin{array}{ccc}-2 & 3 & -9\\7 & 91 & -79\\-6 & -90 & 79\end{array}\right]$$$A