[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 .