Dachprodukt/R^3/Vereinfache/1/Aufgabe/Lösung

Es ist

${}{\begin{aligned}&\,\,\,\,\,\,\,e_{1}\wedge (e_{2}-4e_{3})-e_{2}\wedge (5e_{1}+3e_{2}-4e_{3})+{\left(7e_{3}\right)}\wedge e_{1}-4{\left(5e_{1}\wedge 2e_{3}\right)}+(2e_{1}-8e_{2})\wedge (2e_{1}-8e_{2})\\&=e_{1}\wedge e_{2}-4e_{1}\wedge e_{3}-5e_{2}\wedge e_{1}+4e_{2}\wedge e_{3}+7e_{3}\wedge e_{1}-40e_{1}\wedge e_{3}\\&=e_{1}\wedge e_{2}-4e_{1}\wedge e_{3}+5e_{1}\wedge e_{2}+4e_{2}\wedge e_{3}-7e_{1}\wedge e_{3}-40e_{1}\wedge e_{3}\\&=6e_{1}\wedge e_{2}-51e_{1}\wedge e_{3}+4e_{2}\wedge e_{3}\,\end{aligned}}$

Zur gelösten Aufgabe