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can anyone tell me the reason why if the number of basis is equal to the...

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Advance Math

can anyone tell me the reason why if the number of basis isequal to the dimension of a vector space V then it is the basis ofthe vector space V. and also what the theorem is? since, I think ifV=span{(1,0,0), (0,1,0)} and dim(V)=2 and basis={(1,0,0), (0,0,1)}which the number is also 2. but it is not the basis of V. So, canyou tell where is the mistake. THANK YOU!

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