Let V be the set of all positive real numbers. Determine whether V isa vector space with the operations below: x+y=xy (additon), cx=x^c (multiplication)

Question

anonymous · Answer

I think it is,  I checked all 10 requirements in the definition of vec space,  all satisfied

anonymous · Answer

i dont think the distribution of scalars over "addition" holds.

If c is a scalar in a field, and x and y are vectors, then c(x+y) should equal cx+cy.  But the above definition of "addition" doesnt satisfy that.

c(x+y)= cxy
cx+cy=cxy
c^2xy=cxy  (false)

anonymous · Answer

I fond the questions online actually and it does

c(x+y)=c(xy)=(xy)^c=x^c y^c = x^c+y^c = cx +cy

anonymous · Answer

Yes  I just wanna point this out