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Math Help - union and intersection of bases

  1. #1
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    union and intersection of bases

    I know thsi may seem very simple but i at a loss,

    if i have two bases S and T
    with the union being R and the intersection being Y

    can i say that R is linearluy independent and Y is not??????

    also if anyen cold give me a defintion for the union of vectorspaces it would be much appreciated!!!!!
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  2. #2
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    Quote Originally Posted by calculusgeek View Post
    with the union being R and the intersection being Y
    The union is not necessary linearly independent.
    Let S = \{ \bold{i},\bold{j}\} and T = \{ 2\bold{i},2\bold{j}\} as basis for \mathbb{R}^2.
    Clearly, S\cup T is not linearly independent.

    Now if S,T are basis and S\cap T is non-empty then it is non-empty subset of a linearly independent set therefore it itself must be linearly independent.
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