 Notice that if not all of the scalars are zero, then at least one is non-zero, say formula_5, in which case this equation can be written in the form
Thus, formula_7 is shown to be a linear combination of the remaining vectors.A sequence of vectors formula_8 is said to be "linearly independent" if the equation
can only be satisfied by formula_10 for formula_11.This implies that no vector in the sequence can be represented as a linear combination of the remaining vectors in the sequence.