Chapter 4.3, Problem 1P

Problems

Let $S=\left\{x\in {ℝ}^3:x=\left(r-2s,3r+s,s\right),r,s\in ℝ\right\}$

(a) Show that $S$ is a subspace of ${ℝ}^3$.

(b) Show that the vector in $S$ lie on the plane with equation $3x-y+7z=0$.