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!