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Math Help - Basis

  1. #1
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    Basis

    How do You Solve this problem?

    Let W be the subspace of R^(4) spanned by vectors (1,-2,5,3)^(T),
    (2,3,1,-4)^(T), (3,8,-3,-5)^(T). Extend the basis of W to a basis of the whole space of R^(4).
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  2. #2
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    Heeeelp! Pleeeease!Somebody! Anybody!!!
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  3. #3
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    Quote Originally Posted by googoogaga View Post
    How do You Solve this problem?

    Let W be the subspace of R^(4) spanned by vectors (1,-2,5,3)^(T),
    (2,3,1,-4)^(T), (3,8,-3,-5)^(T). Extend the basis of W to a basis of the whole space of R^(4).
    Well, if W has 3 basis vectors, then it must define a hyperplane of \mathbb{R}^4. Thus use the dot product to find a vector in \mathbb{R}^4 that is perpendicular to each of the basis vectors of W.

    -Dan
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