R^3/(4,-1,2) /wedge (3,5,-6)/Standardbasis/Aufgabe/Lösung

Es ist

${}{\begin{aligned}{\begin{pmatrix}4\\-1\\2\end{pmatrix}}\wedge {\begin{pmatrix}3\\5\\-6\end{pmatrix}}&=(4e_{1}-e_{2}+2e_{3})\wedge (3e_{1}+5e_{2}-6e_{3})\\&=20e_{1}\wedge e_{2}-24e_{1}\wedge e_{3}-3e_{2}\wedge e_{1}+6e_{2}\wedge e_{3}+6e_{3}\wedge e_{1}+10e_{3}\wedge e_{2}\\&=20e_{1}\wedge e_{2}-24e_{1}\wedge e_{3}+3e_{1}\wedge e_{2}+6e_{2}\wedge e_{3}-6e_{1}\wedge e_{3}-10e_{2}\wedge e_{3}\\&=23e_{1}\wedge e_{2}-30e_{1}\wedge e_{3}-4e_{2}\wedge e_{3}.\end{aligned}}$

Zur gelösten Aufgabe