Kunnskapsgnist
Minioren $M_{ij}$ til $a_{ij}$ i $A$ er determinanten til matrisen du får når du stryker rad $i$ og kolonne $j$ i matrise $A$.
$$M_{ij} = \left| \begin{array}{cccc} a_{11} & a_{12} & \cdots & \textcolor{red}{\cancel{\textcolor{black}{a_{1j}}}} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & \textcolor{red}{\cancel{\textcolor{black}{a_{2j}}}} & \cdots & a_{2n} \\ \vdots & \vdots && \vdots && \vdots \\ \textcolor{red}{\cancel{\textcolor{black}{a_{i1}}}} & \textcolor{red}{\cancel{\textcolor{black}{a_{i2}}}} & \cdots & \textcolor{red}{\cancel{\textcolor{black}{a_{ij}}}} & \cdots & \textcolor{red}{\cancel{\textcolor{black}{a_{in}}}} \\ \vdots & \vdots && \vdots && \vdots \\ a_{m1} & a_{m2} & \cdots & \textcolor{red}{\cancel{\textcolor{black}{a_{mj}}}} & \cdots & a_{mn} \end{array} \right|$$Vi bruker miniorer når vi finner determinanter og kofaktorer.
Kofaktoren $C_{ij}$ til $a_{ij}$ i $A$ er gitt ved:
$$C_{ij} = (-1)^{i+j} M_{ij}$$Vi kan sette alle kofaktorene inn i en kofaktormatrise:
$$C = \left( \begin{array}{cccc} C_{11} & C_{12} & \cdots & C_{1n} \\ C_{21} & C_{22} & \cdots & C_{2n} \\ \vdots & \vdots & & \vdots \\ C_{m1} & C_{m2} & \cdots & C_{mn} \end{array} \right)$$Vi bruker kofaktorer når vi finner determinanter og inverse matriser.
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