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Math Help - Vector space

  1. #1
    Newbie lmschneider's Avatar
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    Vector space

    Let U be the set of all vectors in R3 that are perpendicular to a vector u. Prove that U is a vector space.

    I have no idea where to even start. :S
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  2. #2
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    It is enough to show that U is a subspace.
    You need to check that if a,b in U and ka in U for every real number k
    (i.e., need to check if you have two vectors that perpendicular to u, then the sum of these vectors still perpendicular to u and if you have a vector that perpendicular to u then the scalar multiple of the vector still perpendicular to u)
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lmschneider View Post
    Let U be the set of all vectors in R3 that are perpendicular to a vector u. Prove that U is a vector space.

    I have no idea where to even start. :S
    start with verifying that U has all the properties of a vector space. this is just going through a check list.

    the problem is, what kind of creatures do we check? well, two vectors are perpendicular if their dot product is zero. so that gives you a way to characterize the vectors in U, and now we know what to perform our checklist with
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  4. #4
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    Suppose the W & V are both vectors that are orthogonal to U and that s is a scalar.
    What is \left( {sW + V} \right) \cdot U?
    If it is zero then how does that prove subspace??
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