\babel@toc {ngerman}{}
\contentsline {chapter}{\numberline {1}Lineare Algebra}{3}{chapter.1}%
\contentsline {section}{\numberline {1.1}Vektoren in der Ebene - Übersicht}{3}{section.1.1}%
\contentsline {subsection}{\numberline {1.1.1}Veranschaulichung von Vektoren in der Ebene}{3}{subsection.1.1.1}%
\contentsline {subsection}{\numberline {1.1.2}Menge aller Vektoren in der Ebene}{3}{subsection.1.1.2}%
\contentsline {subsection}{\numberline {1.1.3}Addition von Vektoren in der Ebene}{3}{subsection.1.1.3}%
\contentsline {subsection}{\numberline {1.1.4}Nullvektor in der Ebene}{4}{subsection.1.1.4}%
\contentsline {subsection}{\numberline {1.1.5}Subtraktion von Vektoren in der Ebene}{4}{subsection.1.1.5}%
\contentsline {subsection}{\numberline {1.1.6}Multiplikation von einem Vektor mit einem Skalar (einer Zahl)}{5}{subsection.1.1.6}%
\contentsline {subsection}{\numberline {1.1.7}"`Kanonische"' Basisvektoren in der Ebene}{6}{subsection.1.1.7}%
\contentsline {subsection}{\numberline {1.1.8}Lineare Abhängighängigkeit (Kollinearität)}{6}{subsection.1.1.8}%
\contentsline {subsection}{\numberline {1.1.9}Länge (Norm) eines Vektors in der Ebene}{6}{subsection.1.1.9}%
\contentsline {subsection}{\numberline {1.1.10}Einheitsvektoren}{7}{subsection.1.1.10}%
\contentsline {subsection}{\numberline {1.1.11}Skalarprodukt von zwei Vektoren in der Ebene}{7}{subsection.1.1.11}%
\contentsline {subsection}{\numberline {1.1.12}Öffnungswinkel zwischen zwei Vektoren $\vec {a}\neq 0$, $\vec {b}\neq 0$ in der Ebene}{7}{subsection.1.1.12}%
\contentsline {section}{\numberline {1.2}Aufgaben}{8}{section.1.2}%
\contentsline {subsection}{\numberline {1.2.1}Aufgabe 1}{8}{subsection.1.2.1}%
\contentsline {section}{\numberline {1.3}Vektoren im Raum und n-dimensionale Vektoren - Übersicht}{9}{section.1.3}%
\contentsline {subsection}{\numberline {1.3.1}Veranschaulichung von Vektoren im Raum}{9}{subsection.1.3.1}%
\contentsline {subsection}{\numberline {1.3.2}Menge aller Vektoren im Raum / Menge aller n-dimensionalen Vektoren}{10}{subsection.1.3.2}%
\contentsline {subsection}{\numberline {1.3.3}Addition von n-dimensionalen Vektoren}{10}{subsection.1.3.3}%
\contentsline {subsection}{\numberline {1.3.4}n-dimensionaler Nullvektor}{10}{subsection.1.3.4}%
\contentsline {subsection}{\numberline {1.3.5}Subtraktion von n-dimensionalen Vektoren}{10}{subsection.1.3.5}%
\contentsline {subsection}{\numberline {1.3.6}Multiplikation von einem n-dimensionale Vektor mit einem Skalar}{10}{subsection.1.3.6}%
\contentsline {subsection}{\numberline {1.3.7}"`Kanonische"' n-dimensionale Basisvektoren}{11}{subsection.1.3.7}%
\contentsline {subsection}{\numberline {1.3.8}Eine Linearkombination von m n-dimensionalen Vektoren $\vec {a_1},\ldots ,\vec {a_m }$}{11}{subsection.1.3.8}%
\contentsline {subsection}{\numberline {1.3.9}Lineare Abhängigkeit von n-dimensionalen Vektoren}{11}{subsection.1.3.9}%
\contentsline {subsection}{\numberline {1.3.10}Länge (Norm) eines n-dimensionalen Vektors}{11}{subsection.1.3.10}%
\contentsline {subsection}{\numberline {1.3.11}n-dimensionale Einheitsvektoren}{11}{subsection.1.3.11}%
\contentsline {subsection}{\numberline {1.3.12}Skalarprodukt von zwei n-dimensionalen Vektoren}{12}{subsection.1.3.12}%
\contentsline {chapter}{\numberline {2}Lösungen}{13}{chapter.2}%
\contentsline {section}{\numberline {2.1}Aufgabe 1}{13}{section.2.1}%
\contentsline {section}{\numberline {2.2}Aufgabe 120}{13}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}Lösung}{14}{subsection.2.2.1}%
\contentsline {section}{\numberline {2.3}Aufgabe 125}{14}{section.2.3}%
\contentsline {subsection}{\numberline {2.3.1}Lösung}{14}{subsection.2.3.1}%
\contentsline {section}{\numberline {2.4}Aufgabe 127}{15}{section.2.4}%
\contentsline {subsection}{\numberline {2.4.1}Lösung}{15}{subsection.2.4.1}%