Let $W = \{ (x,y,z) \in \mathbb{R}^3 : x-y+z=0 \}$.
a) Is $W$ a subspace of $\mathbb{R}^3$?
b) Find a spanning set for $W$. Give a complete geometric description of $W$.
Let $W = \{ (x,y,z) \in \mathbb{R}^3 : x-y+z=0 \}$.
a) Is $W$ a subspace of $\mathbb{R}^3$?
b) Find a spanning set for $W$. Give a complete geometric description of $W$.