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Math Help - Subspace- Urgent

  1. #1
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    Subspace- Urgent

    Given H = {P = p(t) \in P_3 : p(2) = 0}

    Is H a subspace of P_3?

    Prove the 3 properties of subspace (0 in H, closed under add./mult.) or show an example that violates a property.

    NOTE: P means vector.
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  2. #2
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    yes

    p(2) = 0 => a*p(2)=0
    p(2) = 0 and q(2) = 0 => p(2)+q(2) = 0
    p(x) = 0 is in H
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  3. #3
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    Quote Originally Posted by badgerigar View Post
    p(2) = 0 => a*p(2)=0
    p(2) = 0 and q(2) = 0 => p(2)+q(2) = 0
    p(x) = 0 is in H
    Where in the world do you get q(t)? That is, q(2)?
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  4. #4
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    Notice p is a polynomial..but I don't know how you get q...
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  5. #5
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    .

    p and q are arbitrary elements of H. What you are showing is that H is closed under addition and multiplication by a scalar and is non-empty ie.

    p is an element of H and q is an element of H => p+q is an element of H

    and

    p is an element of H => a*p is an element of H for an arbitrary scalar 'a'

    and

    there exists p such that p is an element of H.

    This is the very basics of subspaces, so I suggest you talk to your teacher if you don't recognise what I am saying.
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