Answer
a) $(0,6 t, t,-t) =t(0,6,1,-1)$, hence $S=\{(0,6,1,-1)\}$ is a basis for $W$.
b) The dimension of $W$ is $1$.
Work Step by Step
Assume the subspace $W=\{(0,6 t, t,-t) : t \text { is a real number }\}$, then
a) $(0,6 t, t,-t) =t(0,6,1,-1)$, hence $S=\{(0,6,1,-1)\}$ is a basis for $W$.
b) The dimension of $W$ is $1$.
