Question

Pe multimea R³ se defineste legea de compozitie $( x_{1}, y_{1}, z_{1})*( x_{2}, y_{2}, z_{2}) = ( x_{1} + x_{2}, y_{1} + y_{2}, z_{1} *z_{2} )$
Gasiti elementul neutru.
Select one:
a. (1,1,0)
b. (0,1,1)
c. (0,1,0)
d. (0,0,1)
e. (1,0,0)
f. (1,0,1)

Answer 1

[tex](x,y,z)*(e_1,e_2,e_3)=(x,y,z)=>(x+e_1,y+e_2,z \cdot e_3)=(x,y,z)\\ x+e_1=x=>e_1=0\\ y+e_2=y=>e_2=0\\ z \cdot e_3=z=>e_3=1\\ (e_1,e_2,e_3)=(0,0,1)[/tex]