## anonymous 4 years ago Determine if V is a vector space when: x+y=xy cx=x^c If not state all the vector axioms it fails

1. anonymous

If yes verify each vector space axiom

2. TuringTest

here's at least one that fails$c(\vec u+\vec v)\neq c\vec u+c\vec v$

3. anonymous

ok what abt tat scaler multiplication?

4. phi

x^c is not a linear operation

5. anonymous

okkkkk

6. TuringTest

actually it's consistent though... $c(\vec u+\vec v)= c\vec u+c\vec v$because we have$c(\vec u+\vec v)=(uv)^c=u^cv^c= c\vec u+c\vec v$so I don't see what's wrong with it

7. anonymous

well it is definitely not closed under scaler multilication though

8. TuringTest

how so?

9. anonymous

because x^c is exponential

10. TuringTest

but that doesn't necessarily take it out of V

11. TuringTest

*the vector space I mean

12. anonymous

oh ya? ok I dont get a thing, I feel so stupid

13. TuringTest

aha! it is a vector space I thought I'd seen it befor check it out, the zero vector turns out to be 1 I think http://tutorial.math.lamar.edu/Classes/LinAlg/VectorSpaces.aspx

14. anonymous

yay lol :D

15. phi

@Tur how do you get from (uv)^c to cu + cv?

16. TuringTest

check out example 5

17. anonymous

yup i see it. Thanks :D

18. TuringTest

@ phi that is what you get when you put the two rules together the exponent is distributed because vector addition is defined as multiplication

19. phi

20. anonymous

LOL i htink i am fundamentally lacking basic knowledge

21. TuringTest

I'm not so good at this stuff, I had it wrong at first as well