Answer
See below
Work Step by Step
Assume $V=R^2$ and the spanning set for a vector space $S=\{(1,0);(0,1);(1,1)\}$
then the vector $v=(2,2)$ can be expressed as a linear combination of the vectors in $S$ such as:
$v=2(1,1)$ or $v=2(1,0)+2(0,1)$
Hence, the statement is false.
