Answer
$S$ is not a subspace
Work Step by Step
$S$ is not a subspace. Since, if $\left[\begin{array}{r}{1}\\ {1}\end{array}\right]\in S$ then take $c=-1$ and so $c\left[\begin{array}{r}{1}\\ {1}\end{array}\right]=-\left[\begin{array}{r}{1}\\ {1}\end{array}\right]=\left[\begin{array}{r}{-1}\\ {-1}\end{array}\right]\notin S$.
