Hi guys i just had a quick question re shilov linear algebra page 44 here he shows that for an 'n' dimentional linear(vector) space K, a subspace, say L, must have dimention no greater than 'n'. He then goed onto say that if a basis is chosen in the subspace L, say f1,f2,...,fr, then additional vectors can be chosen from the linear space K, say f(r+1),...,fn such that f1,f2,...,fr,...,fn form a basis for K. Which makes perfect sense. But here is the part that throws me: Suppose we have the relation: c1f1+c2f2+...+crfr+c(r+1)f(r+1)=0 Where the c terms are constants and f(r+1) is an additional vector from K added to the basis of L. He says if c(r+1) does not equal zero then then L is K. Which is true. But then he says if c(r+1)=0 then the vectors f1,f2,...,fr are linearly dependent, which would be a contradiction. How can this be true? If this is the basis for L and we set it equal to zero then we have all the constants equal to zero, hence they will be linearly independent. I checked the errata and there was no mention of this. Any help will be appreciated, thanks guys.