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z7{h!65tDU3e~5_jx(DnHq?NSiG6=#04ZJF^vwIW=KPx*x}uCRE3TyDAa6lCw2FIw>Pua}iJ{3p{gw<#b`?)^>Q=Yx}f;ae0zsVwv( zr9SsTC;`+PFokof?3%=@_w`u7yiJf#>ZffAXew92CZAVoQal&>JZPTajU-L=s29?+ zs1I}SZ{Z;vD*nK{1=kdRklBMPh(DOG!>z>O`h9-=f3M_6So;6QAHu1`A0GR>7(MST zA~vbkUPbJ$ngQ&?0xJvbnH?jiYkLhG7-K5P8=)$2Rbe~D=mC3nWt6#l(p!e57=Jrbhh;uu;a0qaO N1)sC9C~LoZ{y#tec$WYG diff --git a/docs/loesungen.tex b/docs/loesungen.tex index 58aafc7..53b749c 100644 --- a/docs/loesungen.tex +++ b/docs/loesungen.tex @@ -6482,13 +6482,13 @@ Das Hauptziel hier ist, eine Variant anzubieten, gegen die man seine Versuche ve &\psi(\sum_{i=1}^{d}c_{i}w_{i})=\zerovector\\ &&\text{wegen Linearität von $\psi$}\\ &\Longrightarrow - &\sum_{i=1}^{d}c_{i}w_{i}\in\ker(\psi)=\{\zerovector\}\\ - &&\text{wegen \uline{Injektivität} von $\psi$ + \cite[Lemma~6.1.4]{sinn2020}}\\ + &\sum_{i=1}^{d}c_{i}w_{i}\in\ker(\psi)\\ &\Longrightarrow - &\sum_{i=1}^{d}c_{i}w_{i}=\zerovector\\ + &\sum_{i=1}^{d}c_{i}w_{i}=\zerovector\\ + &&\text{wegen \uline{Injektivität} von $\psi$ + \cite[Lemma~6.1.4]{sinn2020}}\\ &\Longrightarrow &c_{1},c_{2},\ldots,c_{d}=0_{K}\\ - &&\text{weil ${(x_{1},x_{2},\ldots,x_{d})}$ linear unabhängig ist.}\\ + &&\text{weil ${(w_{1},w_{2},\ldots,w_{d})}$ linear unabhängig ist.}\\ \end{longmathe} Damit gilt