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Abgabefristen hochgeladen. -Der Zweck dieser Lösungen ist es vielmehr, Ansätze zu präsentieren, +(Diese werden natürlich \emph{nach} Abgabefristen hochgeladen.) +Der Zweck dieser Lösungen besteht darin, Ansätze zu präsentieren, mit denen man seine eigenen Versuche vergleichen kann. %% ******************************************************************************** @@ -5421,10 +5421,10 @@ Seien $n\in\ntrlpos$ und $\mathbf{v}_{i}\in V$ für $i\in\{1,2,\ldots,n\}$. \end{mathe} Wir haben nun ein Erzeugendensystem bestimmt. - Diese Menge muss auf eine maximale linear unabhängige reduziert werden, + Diese Menge muss auf eine \emph{maximale linear unabhängige Teilmenge} reduziert werden, um eine Basis daraus zu berechnen. - Um diese zu tun, reicht es aus, - die Vektoren in ein homogenes LGS zu überführen, + Hierfür reicht es aus, + die Vektoren in ein homogenes LGS überzuführen, die Matrix auf Zeilenstufenform zu reduzieren, um etwa durch die Spalten entsprechend den freien Unbekannten zu bestimmen, welche Spalten linear abhängig sind. @@ -5523,7 +5523,7 @@ Seien $n\in\ntrlpos$ und $\mathbf{v}_{i}\in V$ für $i\in\{1,2,\ldots,n\}$. \right\}\\ \end{mathe} - als Basis für $U_{1}+U_{2}$ verwenden. + als \fbox{Basis für $U_{1}+U_{2}$} verwenden. \textbf{Bemerkung.} In diesem letzten Teil hatten wir Glück. Wenn sich $\dim(U_{1}+U_{2})