Answer
a) $(s+4 t, t, s, 2 s-t)=s(1,0,1,2)+t(4,1,0,-1)$, hence $S=\{(1,0,1,2),(4,1,0,-1)\}$ is a basis for $W$.
b) The dimension of $W$ is $2$.
Work Step by Step
Assume the subspace $W=\{(s+4 t, t, s, 2 s-t) : s \text { and } t \text { are real numbers }\}$, then
a) $(s+4 t, t, s, 2 s-t)=s(1,0,1,2)+t(4,1,0,-1)$, hence $S=\{(1,0,1,2),(4,1,0,-1)\}$ is a basis for $W$.
b) The dimension of $W$ is $2$.
