ercagpince
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[SOLVED] a simple vector space problem
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 .
all equations defining a vector space
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 .
Homework Statement
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 .
Homework Equations
all equations defining a vector space
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 .