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Folglich sind $\mathbf{v}_{1},\mathbf{v}_{2},\ldots,\mathbf{v}_{n}$ linear unabhängig. @@ -5098,7 +5098,7 @@ Seien $n\in\ntrlpos$ und $\mathbf{v}_{i}\in V$ für $i\in\{1,2,\ldots,n\}$. &= &\zerovector.\\ \end{mathe} - Darum ist gilt die behauptete Implikation nicht im Allgemeinen. + Darum gilt die behauptete Implikation nicht im Allgemeinen. \end{proof} %% AUFGABE 7-3d @@ -5154,7 +5154,7 @@ Seien $n\in\ntrlpos$ und $\mathbf{v}_{i}\in V$ für $i\in\{1,2,\ldots,n\}$. &\forall{j\in\{1,2,\ldots,n\}:~}\alpha_{j}=0\\ \end{longmathe} - Darum ist gilt $\alpha_{i}=0$ für alle $i\in\{1,2,\ldots,n\}$. + Darum gilt $\alpha_{i}=0$ für alle $i\in\{1,2,\ldots,n\}$. Folglich sind $\mathbf{u},\mathbf{v}_{2},\ldots,\mathbf{v}_{n}$ linear unabhängig.