Matriser og ligningssett: Matrisealgebra

Hvordan multipliseres en matrise med en skalar?

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)