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M0464RO$EUJ0CUHKLI3~& diff --git a/4-3.tex b/4-3.tex index 6b721ae..8896461 100644 --- a/4-3.tex +++ b/4-3.tex @@ -27,7 +27,7 @@ Zwei Geraden können parallel sein, dann gibt es keinen Schnittpunkt. Wenn sie i \subsubsection*{Aufgabe 4} \begin{enumerate}[label=\alph*)] \item Ein LGS heisst regulär, wenn die Lösungsmenge genau ein Tupel enthält. -\item Ein LGS heisst regulär, wenn die Lösungsmenge leer ist oder unendlich viele Tupel enthält. +\item Ein LGS heisst singulär, wenn die Lösungsmenge leer ist oder unendlich viele Tupel enthält. \end{enumerate} \subsubsection*{Aufgabe 5} @@ -183,4 +183,25 @@ Einsetzen in I, ergibt $x=2$. Der Zug besteht aus einer Lokomotive zweier Güterwagen und aus acht Personenwagen. \end{enumerate} + + +\subsubsection*{Aufgabe 3} +Die Kurve von I ist ein Kreis um den Ursprung mit Radius 3. (Satz vom Pythagoras) + +II: $y=-x+3$ ist linear. + +Zeichnet man beides ein findet man genau zwei Schnittpunkte. $\mathbb{L}=\{(-3,0),(0,3)\}$ + + +\subsubsection*{Aufgabe 4} +\begin{enumerate} +\item Normalform\\ +\begin{tabular}{r|r@{$~=~$}l} +I&$5x-2y-2z$&$8$\\ +II&$2x+7y+z$&$11$\\ +III&$5x+-2y-2z$&$8$ +\end{tabular} + +Wir sehen nun, dass I und III identisch sind. I+2II ergibt ein 1x2-LGS und ist somit singulär mit unendlich vielen Lösungen. +\end{enumerate} \end{document} \ No newline at end of file