Question

Check whether & is vector space where.
V = {(x,y / x,y€ R} or (x,y) , (x2,y2) €V, (x1, y1) + (x2,y2) = (x1,y1) and for alpa€R, alpha(x1y1)= (alpha x1= alpha y1) ​

Answer 1

Answer:

Just trying to figure this problem out.Which one of the 10 axioms does (x,y) x,y E R not satisfy. I've tried associative multiplication and associative addition as answers but been incorrect

Let VV be the set {(x,y)∣x,y∈R}{(x,y)∣x,y∈R} with addition operation ⊕⊕ defined by

(x1,y1)⊕(x2,y2)=(x1+x2,y1y2)

(x1,y1)⊕(x2,y2)=(x1+x2,y1y2)

and scalar multiplication ⊙⊙ defined by

α⊙(x,y)=(x,0).

α⊙(x,y)=(x,0).

Show that VV is not a vector space by determining which of the 1010 v