Answer
a) $W$ is the plane in $R^3$ given by the equation $x=2y-z$ and passing through the origin.
b) $(2 s-t, s, t)=s(2,1,0)+t(-1,0,1)$, hence $S=\{(2,1,0),(-1,0,1)\}$ is a basis for $W$.
c) The dimension of $W$ is $2$.
Work Step by Step
Assume the subspace $W=\{(2 s-t, s, t) : s \text { and } t \text { are real numbers }\}$, then
a) $W$ is the plane in $R^3$ given by the equation $x=2y-z$ and passing through the origin.
b) $(2 s-t, s, t)=s(2,1,0)+t(-1,0,1)$, hence $S=\{(2,1,0),(-1,0,1)\}$ is a basis for $W$.
c) The dimension of $W$ is $2$.
