Matriser og ligningssett: Matrisealgebra

Hvordan legges to matriser sammen?

USN

Addisjon: Legg sammen korresponderende elementer i to matriser med lik dimensjon:

$$\left( \begin{array}{cccc} \textcolor{red}{a_{11}} & \cdots & \textcolor{red}{a_{1n}} \\ \textcolor{red}{a_{21}} & \cdots & \textcolor{red}{a_{2n}} \\ \vdots & & \vdots \\ \textcolor{red}{a_{m1}} & \cdots & \textcolor{red}{a_{mn}} \\ \end{array} \right) + \left( \begin{array}{cccc} \textcolor{blue}{b_{11}} & \cdots & \textcolor{blue}{b_{1n}} \\ \textcolor{blue}{b_{21}} & \cdots & \textcolor{blue}{b_{2n}} \\ \vdots & & \vdots \\ \textcolor{blue}{b_{m1}} & \cdots & \textcolor{blue}{b_{mn}} \\ \end{array} \right) = \left( \begin{array}{cccc} \!\textcolor{red}{a_{11}} + \textcolor{blue}{b_{11}} & \cdots & \!\textcolor{red}{a_{1n}} + \textcolor{blue}{b_{1n}} \\ \!\textcolor{red}{a_{21}} + \textcolor{blue}{b_{21}} & \cdots & \!\textcolor{red}{a_{2n}} + \textcolor{blue}{b_{2n}} \\ \vdots & & \vdots \\ \!\textcolor{red}{a_{m1}} + \textcolor{blue}{b_{m1}} & \cdots & \!\textcolor{red}{a_{mn}} + \textcolor{blue}{b_{mn}} \\ \end{array} \!\! \right) $$

Differanse: Finn differansen mellom korresponderende elementer i to matriser med lik dimensjon:

$$\left( \begin{array}{cccc} \textcolor{red}{a_{11}} & \cdots & \textcolor{red}{a_{1n}} \\ \textcolor{red}{a_{21}} & \cdots & \textcolor{red}{a_{2n}} \\ \vdots & & \vdots \\ \textcolor{red}{a_{m1}} & \cdots & \textcolor{red}{a_{mn}} \\ \end{array} \right) - \left( \begin{array}{cccc} \textcolor{blue}{b_{11}} & \cdots & \textcolor{blue}{b_{1n}} \\ \textcolor{blue}{b_{21}} & \cdots & \textcolor{blue}{b_{2n}} \\ \vdots & & \vdots \\ \textcolor{blue}{b_{m1}} & \cdots & \textcolor{blue}{b_{mn}} \\ \end{array} \right) = \left( \begin{array}{cccc} \!\textcolor{red}{a_{11}} - \textcolor{blue}{b_{11}} & \cdots & \!\textcolor{red}{a_{1n}} - \textcolor{blue}{b_{1n}} \\ \!\textcolor{red}{a_{21}} - \textcolor{blue}{b_{21}} & \cdots & \!\textcolor{red}{a_{2n}} - \textcolor{blue}{b_{2n}} \\ \vdots & & \vdots \\ \!\textcolor{red}{a_{m1}} - \textcolor{blue}{b_{m1}} & \cdots & \!\textcolor{red}{a_{mn}} - \textcolor{blue}{b_{mn}} \\ \end{array} \!\! \right) $$

Gauss-Jordan eliminasjon og redusert trappeform Oppgaver Multipliser med konstant