Results 1 to 3 of 3

Math Help - Easy Linear Algebra Question

  1. #1
    Member
    Joined
    Apr 2010
    Posts
    133

    Easy Linear Algebra Question

    Hey guys! New year new math class. I'm in Linear Algebra and its been quite a few years since ive taken the intro to linear alg course so i'm a little rusty and don't have that book any more. In the following question i'm not quite certain how to approach this problem. The problem states:

    A real-valued function f defined on the real line is called an even functions if f(-t)=f(t) for each real number t. Prove that the set of even functions defined on the real line with the operations of addition and scalar multiplication defined in the previous example is a vector space.

    Previous Example: Let S be any nonempty set and F be and field, ad let F(S,F) denote the set of all functions from S to F. Two functions f and g in F(S,F ) are called equal if f(s)=g(s) for each s in S. The set F(S,F) is a vector space with the operations of addition and scalar multiplication defined for f,g in F(S,F) and c in F by: (f+g)(s)=f(s)+g(s) and (cf)(s)=c[f(s)] for each s in S.

    I'm just not sure what to do :/. Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    This will work:
    (f+\alpha g)(-x)=f(-x)+ \alpha g(-x)= f(x)+ \alpha g(x)=(f+\alpha g)(x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,372
    Thanks
    1314
    Using what you wrote you could show that if f(-x)= f(x) and g(-x)= g(x) then (f+ g)(-x)= f(-x)+ g(-x)= f(x)+ g(x)= (f+ g)(x) and then that (\alpha f)(-x)= \alpha f(-x)= \alpha f(x)= (\alpha f)(x). What Plato did was combine those two into one equation.

    (I am using (f+ g) and (\alpha f) to mean the functions formed by adding f and g and by multiplying f by the number \alpha. Of course, those are defined by (f+ g)(x)= f(x)+ g(x) and (\alpha f)(x)= \alpha f(x).)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Easy question about linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 16th 2011, 01:35 PM
  2. Easy Linear Algebra Proofs
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: July 8th 2010, 06:22 AM
  3. Easy algebra question - Quotient rule.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 2nd 2010, 01:37 AM
  4. EAsy algebra question need help!!!
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 18th 2009, 06:34 AM
  5. Easy algebra question need help!!!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 18th 2009, 06:01 AM

Search Tags


/mathhelpforum @mathhelpforum