Når vi multipliserer en matrise med en skalar, multipliseres hvert element i matrisen med skalaren:
\textcolor{red}{k}
\left( \begin{array}{cccc}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{array} \right)
=
\left( \begin{array}{cc}
\textcolor{red}{k} a_{11} & \textcolor{red}{k} a_{12} & \cdots & \textcolor{red}{k} a_{1n} \\
\textcolor{red}{k} a_{21} & \textcolor{red}{k} a_{22} & \cdots & \textcolor{red}{k} a_{2n} \\
\vdots & \vdots & & \vdots \\
\textcolor{red}{k} a_{m1} & \textcolor{red}{k} a_{m2} & \cdots & \textcolor{red}{k} a_{mn}
\end{array} \right) + Kort video
+ Eksempel 1
Multipliser hvert element i matrisen med skalaren:
\textcolor{red}{2}
\left( \begin{array}{cc}
1 & 2 \\ 3 & 4
\end{array} \right)
=
\left( \begin{array}{cc}
\textcolor{red}{2} \cdot 1 & \textcolor{red}{2} \cdot 2 \\
\textcolor{red}{2} \cdot 3 & \textcolor{red}{2} \cdot 4
\end{array} \right)
=
\left( \begin{array}{cc}
2 & 4 \\ 6 & 8
\end{array} \right) + Eksempel 2
Multipliser hvert element i matrisen med skalaren.
\textcolor{red}{k}
\left( \begin{array}{cc}
1 & 2 & 3 \\ 4 & 5 & 6
\end{array} \right)
=
\left( \begin{array}{cc}
\textcolor{red}{k} & 2 \textcolor{red}{k} & 3 \textcolor{red}{k} \\
4 \textcolor{red}{k} & 5 \textcolor{red}{k} & 6 \textcolor{red}{k}
\end{array} \right)