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Math Help - Showing that a non-empty subset M is an affine subset of R^4

  1. #1
    Junior Member
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    Sep 2010
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    Showing that a non-empty subset M is an affine subset of R^4

    Hi, I have to do a project on affine subsets and affine mappings, but I have no clue what they are... We are given only one clue and I can't find many notes on google. I would really appreciate it if someone could help me with this first problem (and if you could also give me a link to some good notes on the topic). Thanks a lot!

    The problem says:

    "To illustrate this concept, show that

    M=\{x=(x_1, ..., x_4) \epsilon \mathbb{R}^4 : 2x_1-x_2+x_3=1 and x_1+4x_3-2x_4=3\}

    is an affine subset of \mathbb{R}^4."

    And the only hint we get is

    "Throughout Part A of this project, V will be a real vector space and, for a non-empty subset S of V and a \epsilon V, the set { x+a : x \epsilon S} will be denoted by S+a.

    An affine subset of V is a non-empty subset M of V with the property that \lambda *x+(1- \lambda )*y \epsilon M whenever x,y \epsilon M and \lambda \epsilon \mathbb{R}."
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  2. #2
    Junior Member
    Joined
    Sep 2010
    Posts
    64

    Re: Showing that a non-empty subset M is an affine subset of R^4

    OK, I have managed to solve the problem... I just have to substitute lambda*x+(1-lambda)*y into both of the conditions given.
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