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Math Help - Vector Space

  1. #1
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    Vector Space

    One of the questions in my text book asks this:

    The set of all pairs of real numbers of the form  (1,x) with the operations (1, y) + (1, y') = (1, y + y') and k(1,y) = (1, ky). The book says this is vector space, but when I check this axiom (k+m)u = ku + mu

    Here is my work:
    <br />
(c + k)(1,x) = (1, (c+k)x) = (1, cx + kx)<br />

    <br />
c(1,x) + k(1,x) = (1,cx) + (1,kx) = (2, cx+kx)<br />

    Where am I going wrong?

    Thanks
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  2. #2
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    Quote Originally Posted by evant8950 View Post
    One of the questions in my text book asks this:
    The set of all pairs of real numbers of the form  (1,x) with the operations (1, y) + (1, y') = (1, y + y') and k(1,y) = (1, ky). The book says this is vector space, but when I check this axiom (k+m)u = ku + mu
    c(1,x) + k(1,x) = (1,cx) + (1,kx) = (2, cx+kx)
    By definition the 1's do not add.
    c(1,x) + k(1,x) = (1,cx) + (1,kx) = (1, cx+kx)
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  3. #3
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    Thanks. Simple mistake on my part.
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