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kwal0203
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Homework Statement
Determine whether the following is a Subspace of r^3:
All vectors of the form (a,b,c), where b=a+c
The Attempt at a Solution
The answer in the book says it is not a subspace but I can only find examples that show it is a Subspace I.e.
Let u=(a,a+c,c)=(1,2,1), v=(a,a+c,c)=(2,4,2) and k=2 then
U+v=(3,6,3)=(a,a+c,c) so it's closed under addition
Ku=2(a,a+c,c)=2(1,2,1)=(2,4,2)=(a,a+c,c) so it is closed under scalar multiplication
Maybe I don't understand the concept correctly am I doing something wrong?