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Math Help - Is S = real space(R^3)

  1. #1
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    Is S = real space(R^3)

    where S = {[ 2a-b, a , b , -a ] | a,b are real numbers}

    how do prove and show this one?
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  2. #2
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    Can you explain what you mean by real space( \mathbb{R}^3). I can't find that terminology in any of my algebra texts.

    Are you asking if S forms a basis for \mathbb{R}^3?
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  3. #3
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    Quote Originally Posted by experiment00 View Post
    where S = {[ 2a-b, a , b , -a ] | a,b are real numbers}

    how do prove and show this one?

    The vector (2a-b,a,b,-a) is 4-dimensional and thus cannot belong to \mathbb{R}^3

    Tonio
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  4. #4
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    The vector (2a-b,a,b,-a) is 4-dimensional and thus cannot belong to \mathbb{R}^{3}.
    In addition, it is a vector with two degrees of freedom (it has two parameters, a and b). And so, considered as a subset of \mathbb{R}^{4}, it is two-dimensional at most.
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