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Homework Help: Show: Vectors e.g.(a,b,1) do not form vector space.

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  1. Aug 12, 2018 at 9:58 AM #1
    1. The problem statement, all variables and given/known data
    upload_2018-8-12_19-29-5.png

    2. Relevant equations
    definition of null vector,
    upload_2018-8-12_19-40-16.png


    3. The attempt at a solution
    null vector : ## |0 \rangle = (0,0,0) ##
    inverse of (a,b,c) = ( - a, -b, -c)
    vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same form. So, the vectors of the form ( a,b,1) do not form a vector space.

    Is this correct?
     
    Last edited: Aug 12, 2018 at 10:12 AM
  2. jcsd
  3. Aug 12, 2018 at 10:22 AM #2

    fresh_42

    User Avatar
    2017 Award

    Staff: Mentor

    Yes, or even easier ##(0,0,0) \notin \{\,(a,b,1)\,\}##.
     
  4. Aug 12, 2018 at 10:51 AM #3
    Thanks for it.
     
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