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A simple vector space problem

  1. Nov 18, 2007 #1
    [SOLVED] a simple vector space problem

    1. The problem statement, all variables and given/known data

    Consider the set of all entities of the form (a,b,c) where the entries are real numbers . Addition and scalar multiplication are defined as follows :
    (a,b,c) + (d,e,f) = (a+d,b+e,c+f)
    z*(a,b,c) = (za,zb,zc)

    Show that vectors of the form (a,b,1) do not form a vector space .

    2. Relevant equations

    all equations defining a vector space

    3. The attempt at a solution

    I managed to find the inverse under addition vector and also the null vector for that vector space , however , I couldn't find any logical explanation or proof why a vector like (a,b,1) do not form a vector space .
  2. jcsd
  3. Nov 18, 2007 #2


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    Homework Helper

    What is the z-component of the resultant vector if you add two of these? Will it still belong to that set of vectors?
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