Answer
True
Work Step by Step
Let $S=\{v_1,v_2,...v_n\}$ be the set of vectors and one of the vectors can be expressed as a linear combination of the others.
We have $v_i=c_1v_1+...c_{i-v}v_{i-v}+c_{i+1}v_{i+1}+...+c_nv_n$
Obtain:
$a_1v_1+a_2v_2+...+a_iv_i+...a_nv_n=0\\
a_1v_1+a_2v_2+...+c_1v_1+...+c_{i-v}v_{i-v}+c_{i+v}v_{i+v}...+c_nv_n+...a_nv_n=0\\
(a_1+c_1)v_1+(a_2+c_2)v_2+...+(a_n+c_n)v_n=0$
The solutions of this can be listed as $a_1=-c_1,...,a_n=-c_n$
We can see that there is a nonzero solution here.
Thus, set $S=\{v_1,v_2,...v_n\}$ is linearly independent.
If it is possible to express one of the vectors in a set $S$ as a linear combination of the others, then $S$ is a linearly dependent set.
