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Math Help - spanning set for R^2

  1. #1
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    Question spanning set for R^2

    First, can anyone explain to me the meaning of spanning set? I am a little confused with it meaning.

    Then please show me how to do the below questions. Thank you very much.

    Determine whether any of the following sets are spanning sets for R^2 , considered as column matrices
    1) S = { esub1 = [1] , esub2 = [0]}
    ........................[0]............. [1]

    2) S = { esub1 = [1] , esub2 = [0], fsub1 = [1]}
    ........................[0]............. [1].............[1]

    3) S = { fsub1 = [1] , fsub2 = [2]}
    .......................[1]............. [2]


    =================
    note: e and f are vectors.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by apple12 View Post
    First, can anyone explain to me the meaning of spanning set? I am a little confused with it meaning.
    A spanning set for a (sub-) space W is a set of elements of W which spans W. A set S \subset W spans W if for all w \in W w is a linear combination of elements of S.

    Then please show me how to do the below questions. Thank you very much.

    Determine whether any of the following sets are spanning sets for R^2 , considered as column matrices
    1) S = { esub1 = [1] , esub2 = [0]}
    ........................[0]............. [1]
    This is the standard basis for R^2, so spans R^2.

    2) S = { esub1 = [1] , esub2 = [0], fsub1 = [1]}
    ........................[0]............. [1].............[1]
    This contains the standard basis and so spans R^2

    3) S = { fsub1 = [1] , fsub2 = [2]}
    .......................[1]............. [2]
    [1,2]' cannot be written as a linear combination of elements of S, so S does not span R^2.

    RonL
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