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Im not exactly sure what you are asking. The smallest subspace is always 0

i tried but do not get the point
plz u proof it if u can...

but subspaces force you to be able to add and multiply any two vectors and remain in the subpsace

from all these how can u say w is SMALLEST subspace?

ok ok Ill do the proof :)

I uppercased set and subspace to make sure you didnt confuse them as you were reading it.

no not nessarly can we take any vi and any vj and have vi + vj NOT an element of our SET

thanks a lot. now i try to understand it