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

can anyone tell me the reason why if the number of basis is equal to the dimension of a vector space V then it is the basis of the vector space V. and also what the theorem is? since, I think if V=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, can you tell where is the mistake. THANK YOU!

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Colby Messinger answered 1 month ago

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