Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof / 6 / b / Solution

The vectors $v_1,\dots ,v_n$ are linearly independent ifThey are linearly dependent if some such relation has at least one nonzero coefficient. All coefficients lie in the underlying field. Thus linear independence means that only the trivial linear combination gives zero; linear dependence means that a nontrivial one does.