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Math Help - Homothetic property

  1. #1
    Member kezman's Avatar
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    Homothetic property

    Please I need your help.
    I need to prove or disprove the following.

    a_1 a_2 real numbers.
    x, y both in R^3.
    A is a convex set in R^3.

    a.x in a.A and b.y in b.A. Then ax + by is in (a+b)A

    (a.A, b.A, (a+b)A are all Homothetic transformations)
    Last edited by kezman; May 1st 2013 at 12:58 AM.
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  2. #2
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    Re: Homothetic property

    Consider the unit vectors v_1=(1,0,0) and v_2=(0,1,0) and the set A=\{a\cdot v_1|a\in \mathbb{R}\}\cup \{b\cdot v_2|2\in \mathbb{R}\}
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  3. #3
    Member kezman's Avatar
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    Re: Homothetic property

    Im sorry I forgot that A is a convex set
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