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Hier wollen wir ein paar Aufgaben komplett durchrechnen. \textbf{Beachte!} Hier geht es niemals darum, -eine lineare Ausdehnung \emph{exmplizit darzustellen}, +eine lineare Ausdehnung \emph{explizit darzustellen}, sondern vielmehr (1) \cite[Satz~6.1.13]{sinn2020} als zentrales Resultat anzuwenden, (2) eine Basis aus den Inputvektoren zu generieren