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Math Help - subspace qustion-exam coming up help!!-i dont understand

  1. #1
    n22
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    subspace qustion-exam coming up help!!-i dont understand

    Hello,
    I would really appreciate it if someone could help me with these questions .
    thanks
    Determine whether or not Q is a subspace of F.

    Let Q ={f which is an element of F such that df(x)/dx=2f(x)


    Also,Determine whether or not P is a subspace of F.
    LetP={f which is an element of F such that df(x)/dx=2x}



    also how do I approach these questions? which ones are vector spaces of F and why?
    F = { f :R−→R | f a function } is a vector space.
    S1 = {f : R → R | f(x) = f(−x) for all x ∈ R}
    S2 = {f : R → R | f(−2) = 0}
    S3 = {f : R → R | f(x) = −2 for all x ∈ R}
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    Re: subspace qustion-exam coming up help!!-i dont understand

    Do you not know how to determine if A is a subspace of vetore space B?
    First A must be a subset of B.
    Then it must be "closed under addition": if u and v are in A then so is u+ v.
    And it must be "closed under scalar multiplication: if v is in A and a is a scalar then av is in A.
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