Hi, I have this problem that is solved, but I don't understand the theory behind it.(adsbygoogle = window.adsbygoogle || []).push({});

It says: Which of the following sets, with the natural definitions of addition and scalar multiplication, form real vector spaces?

A) The set of all differentiable functions [itex]f:(0,1)\rightarrow\Re[/itex] such that [itex]f+f'=0[/itex].

B) The set of all differentiable functions [itex]f:(-1,1)\rightarrow\Re[/itex] such that [itex]f+f'=0[/itex] and [itex]f(0)=1[/itex].

The answer says the first one is a vector space, but that the second one is not because zero does not belong to the set... However, I don't see the reasoning behind it. Maybe they are supposed to be the opposite (A is not a vector space and B is) and the answer is wrong? No one has complained about it and there is nothing on the course forum, so I think the answers should be correct :/

Thanks a lot!

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# Confused with Vector Spaces

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