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Math Help - Subsets that are subspaces of P2

  1. #1
    Junior Member
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    Subsets that are subspaces of P2

    Hello, i recently took a linear algebra test and there was a bonus on it. The bonus was the material that we are going to soon be learning. I have not read ahead so i didnt get it right. I was wondering if you guys could explain it to me.

    Bonus:
    Which of the following subsets of P2 are subspaces of P2?

    A.) p(t)| p'(t)+2p(t)+7=0
    B.) p(t)| p(8)=0
    C.) p(t)| integral from 0-1(p(t)dt)=0
    D.) p(t)| p(7)=4
    E.) p(t)| p'(4)=p(0)
    F.) p(t)| p(-t)=p(t) for all t


    Thank You,
    Diggidy
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  2. #2
    Senior Member Tinyboss's Avatar
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    B, C, E, and F are subspaces. You need to check whether they contain 0 and are closed under addition and scalar multiplication. Keep in mind that the derivative and integral are linear.
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