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Math Help - Is the set a subspace?

  1. #1
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    Is the set a subspace?

    (apology on the format; I don't know the beginning format for latex)

    Is the set W={p (epsilon) C2(-infinity, infinity) | 4p''-6p'+2p=0} a subspace of P2(-inf,inf) with the normal operations of polynomial addition and scalar multiplication?

    Can someone give me some advice on how to start?
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  2. #2
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    Re: Is the set a subspace?

    Could you remind what P2(-inf,inf) is?

    The question seems to ask whether the sum of two solutions of 4p''-6p'+2p=0 is again a solution. Well, differentiation is a linear operator...
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  3. #3
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    Re: Is the set a subspace?

    would W be a subset because P2 contains all real numbers?

    I don't follow where you get the sum of two solutions.
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  4. #4
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    Re: Is the set a subspace?

    I am still not sure what P2(-inf,inf) is.

    WolframAlpha says that the solutions to 4p''-6p'+2p=0 are c_1e^{x/2}+c_2e^x for various c_1,c_2. These are not polynomials unless c_1=c_2=0.

    What I meant is that as a subset of C2(-infinity, infinity), W is a vector space, i..e., it is closed under addition and scalar multiplication. That's why I said that the sum of two solutions is again a solution.
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