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Math Help - [SOLVED] Understanding Spanning

  1. #1
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    [SOLVED] Understanding Spanning

    Hey guys.

    I have a simple question regarding spanning.

    Obviously, if V = {( e_1, e_2, e_3, e_4) | ( e_1, e_2, e_3, e_4) \in R^4}
    V spans R^4.

    Can I say that V spans R^3??
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  2. #2
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    Quote Originally Posted by jayshizwiz View Post
    Hey guys.

    I have a simple question regarding spanning.

    Obviously, if V = {( e_1, e_2, e_3, e_4) | ( e_1, e_2, e_3, e_4) \in R^4}
    V spans R^4.

    Can I say that V spans R^3??

    Of course not: \mathbb{R}^3 is not even a subset of \mathbb{R}^4 and thus no element of V is contained in it!

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Of course not: \mathbb{R}^3 is not even a subset of \mathbb{R}^4 and thus no element of V is contained in it!
    So basically,

    (1,0,0,0) \in R^4

    but

    (1,0,0) is never \in R^4.

    Is it possible do draw a vector with 2 components in a three dimensional space?

    and vice versa,

    can you draw (1,0,0) in a two-dimensional plane???
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  4. #4
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    Quote Originally Posted by jayshizwiz View Post
    So basically,

    (1,0,0,0) \in R^4

    but

    (1,0,0) is never \in R^4.

    Is it possible do draw a vector with 2 components in a three dimensional space?

    and vice versa,

    can you draw (1,0,0) in a two-dimensional plane???
    In \mathbb{R}^2, vectors are of the form (x,y); therefore, how can a vector of the form (x,y,z)\in\mathbb{R}^2?
    Last edited by dwsmith; May 27th 2010 at 08:01 AM.
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  5. #5
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    In , vectors are of the form ; therefore, how can a vector of the form ?
    I dunno. But I would assume a two-dimensional plane (1,3) would be found in the (x,y) plane of (x,y,z) space...

    In everyday life, we live in three-dimensional space containing two-dimensional things...Unless you count time as a 4th dimension...But let's not digress...
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  6. #6
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    Quote Originally Posted by jayshizwiz View Post
    I dunno. But I would assume a two-dimensional plane (1,3) would be found in the (x,y) plane of (x,y,z) space...

    In everyday life, we live in three-dimensional space containing two-dimensional things...Unless you count time as a 4th dimension...But let's not digress...
    (1,3) Is not the same as (1,3,0)
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  7. #7
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    Gotcha,
    Thanks.
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