Elementare Mathematik 2/Gemischte Definitionsabfrage/5/Aufgabe/Lösung

${\displaystyle {}S\subseteq K^{n}}$

${\displaystyle {}S}$

${\displaystyle {}U\subseteq K^{n}}$

${\displaystyle {}P\in K^{n}}$

${\displaystyle {}S=P+U={\left\{P+v\mid v\in U\right\}}\,}$

gibt.

${\displaystyle {}B_{ij}}$

${\displaystyle {}n\times n}$

${\displaystyle {}(i,j)}$

${\displaystyle {}1}$

1. ${\displaystyle {}V_{ij}:=E_{n}-B_{ii}-B_{jj}+B_{ij}+B_{ji}}$.
2. ${\displaystyle {}S_{k}(s):=E_{n}+(s-1)B_{kk}{\text{ für }}s\neq 0}$.
3. ${\displaystyle {}A_{ij}(a):=E_{n}+aB_{ij}{\text{ für }}i\neq j{\text{ und }}a\in K}$.

${\displaystyle {}x}$

${\displaystyle {}\epsilon \in K}$

${\displaystyle {}\epsilon >0}$

${\displaystyle {}n_{0}\in \mathbb {N} }$

${\displaystyle {}n\geq n_{0}}$

${\displaystyle {}\vert {x_{n}-x}\vert \leq \epsilon \,}$

gilt.