## Elementary Linear Algebra 7th Edition

$S$ is linearly independent.
Assume the combination $$a(1,-4,1)+b(6,3,2)=(0,0,0).$$ We have the system \begin{align*} a+6b&=0\\ -4a+3b&=0\\ a+2b&=0. \end{align*} The above system has a unique solution, that is, $$a=0, \quad b=0.$$ Consequently, $S$ is linearly independent.