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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Let S be a non empty set and F be a field, for any S ES define W=lf€F{S, F]:f(s,=0} W=lf€F|S,F}:fls)=0 for all but a finite number of elements of S}, where F(S,
Let S be a non empty set and F be a field, for any S ES define W=lf€F{S, F]:f(s,=0} W=lf€F|S,F}:fls)=0 for all but a finite number of elements of S}, where F(S,F) denotes the set of all functions from S to F. then only W, is a subspace of F(S,F) only W2 is a subspace of F(S,F) Both W, and W, is subspace of F(S,F) Neither W, nor W is subspace of F(S,F)
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Priyadarshan Choursiya
if you have any query, reply me. this question is good. this question involve countability. to make W be subspaces it is needed that it is closed. in general we show that a+b for closeness but actually we need to show that any LC of elements of W belongs to W then it will close. here W2 is not closed under addition, that's why it is not subspace. sometimes we use different different ideas which comes after lot of practice. best of luck
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