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Math Help - Determine if W is a subspace of the vector space V.

  1. #1
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    Determine if W is a subspace of the vector space V.

    Could someone help me out with questions (a) and (c), just the first couple of steps.

    Any help is appreciated!
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  2. #2
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    The axioms are scalar multiplication and vector addition, correct?
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    The axioms are scalar multiplication and vector addition, correct?
    Yes, let me write out the definitions:

    V is the vector space

    addition: If u & v are in V, then u + v is in V

    multiplication: If k is any scalar & u is any object in V, then ku is in V
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  4. #4
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    part c
    \alpha p(x)=\alpha(a+bx^2)=\alpha a + \alpha bx^2 where \alpha \in \mathbb{R}

    Therefore, \alpha a + \alpha bx^2 \in V

    Do addition the same way.
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  5. #5
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    The key to the addition is that a and b aren't negative.
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  6. #6
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    Quote Originally Posted by dwsmith View Post
    The key to the addition is that a and b aren't negative.

    What about the multiplication, if I had something like:

    k(a+bx^2) = ka + kbx^2

    The k could be a negative number, making a and b negative, so the multiplication axiom wouldn't hold?
    Last edited by DarK; October 21st 2010 at 07:02 PM.
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  7. #7
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    If k is negative, a and b are still positive.

    ka=w would be negative.
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  8. #8
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    The reason the problem says that is so this doesn't happen:

    a+bx^2+a+(-bx^2)=2a \not\in V
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  9. #9
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    Ok, that makes alot more sense, thank you!
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