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