Results 1 to 3 of 3

Math Help - Vector space basic proof

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    62

    Vector space basic proof

    Hi everyone,

    how can I show that:


    1. F=C,V ={f∈C[t]|f(0)∈R},
    2. F=R,V ={f∈C[t]|f(0)∈R}.

    are or aren't vectorial spaces? I know the 8 axioms that I'm supposed to use to show it but I don't see how I can use them here.

    Please help.
    Last edited by sunmalus; October 1st 2009 at 09:53 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Quote Originally Posted by sunmalus View Post
    Hi everyone,

    how can I show that:


    1. F=C,V ={f∈C[t]|f(0)∈R},
    2. F=R,V ={f∈C[t]|f(0)∈R}.

    are or aren't vectorial spaces? I know the 8 axioms that I'm supposed to use to show it but I don't see how I can use them here.

    Please help.
    Assume a=f(0) such that f \in V, does ia \in \mathbb{R}? where i= \sqrt {-1} \in \mathbb{C}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,569
    Thanks
    1409
    You know that addition and multiplication of numbers (and the function values are numbers) are commutative, associative, etc. so all you need to determine is if addition and scalar multiplication are closed. That was the point of Jose27's post. For (1) f(0) must be real for all f in the set. But what happens if you multiply by i?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector Space proof
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: June 12th 2011, 06:26 PM
  2. Vector Space Proof
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: June 14th 2009, 10:23 AM
  3. Help with a basic vector proof.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 29th 2009, 02:51 PM
  4. Vector space Proof
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: April 14th 2008, 07:44 PM
  5. Vector space proof
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 13th 2006, 09:55 AM

Search Tags


/mathhelpforum @mathhelpforum