Aufgabe ist zu überprüfen ob die Abbildungen linear sind:
a) \( \Phi_{1}: R[x] \mapsto R, \quad p \mapsto p(1) \)
b) \( \Phi_{2}: R^{3} \mapsto R, \quad\left(x_{1}, x_{2}, x_{3}\right)^{T} \mapsto\left|x_{1}\right|+\left|x_{2}\right|+\left|x_{3}\right| \)
c) \( \Phi_{3}: R^{2} \mapsto R^{2}, \quad(x, y)^{T} \mapsto(3 x y, 9 x)^{T} \)
d) \( \Phi_{4}: R^{2} \mapsto R^{2}, \quad(x, y)^{T} \mapsto(3 x-y, 9)^{T} \)
e) \( \Phi_{5}: R^{3} \mapsto R^{2},\left(\begin{array}{l}x \\ y \\ z\end{array}\right) \mapsto\left(\begin{array}{c}x+2 y+3 z \\ 3 x+2 y+z\end{array}\right) \)