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fleauworld

  • 2 years ago

Let Z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted o, by: alpha o k = [[alpha]].k for all k in Z where [[alpha]] denotes the greatest integer less than or equal to alpha, for example, 2.25 o 4 = [[2.25]].4 =2..4 = 8 show that Z, together with these operations, is not a vector space. Which axioms fail to hold?

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  1. myko
    • 2 years ago
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    Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v

  2. fleauworld
    • 2 years ago
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    I agree with the second answer, but why the Distributivity of scalar multiplication with respect to field addition fail to hold ?

  3. experimentX
    • 2 years ago
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    straight out of wikipedia Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv let a=2.5 and b=3.5

  4. fleauworld
    • 2 years ago
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    oh I see never mind, thx :)

  5. myko
    • 2 years ago
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    let them better be a=2,5 and b=3,6

  6. fleauworld
    • 2 years ago
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    what was ur approach to finding the solutions please ? did you test for all axioms one by one ?

  7. myko
    • 2 years ago
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    not really, becouse all the rest are not afected by any weird definition. Just this two

  8. experimentX
    • 2 years ago
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    the other one also seem to work Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v a=4 and b=2.5

  9. fleauworld
    • 2 years ago
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    hum ok I see, thank you mate

  10. myko
    • 2 years ago
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    you have to choose two numbers where decimal part sum is bigger than 1

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