We know that any four geometric vectors are linearly dependent. Is it true that any n (n >= 4 ) vectors will be linearly dependent? After all, if four vectors are linearly dependent, then one of the vectors is expressed in terms of the others: $\overline{a} = \alpha*\overline{b} + \beta*\overline{c} + \gamma*\overline{d}$
Then if we add any fifth vector (and so on), then the new system will also be linearly dependent, because: $\overline{a} = \alpha*\overline{b} + \beta*\overline{c} + \gamma*\overline{d} + 0*\overline{e}$