Chapter 4.6, Problem 35P

Let $v_1=\left(0,6,3\right)$, $v_2=\left(3,0,3\right)$, and $v_3=\left(6,-3,0\right)$. Show that $\left\{v_1,v_2,v_3\right\}$ is a basis for ${ℝ}^3$. [Hint: You need not show that the set is both linearly independent and a spanning set for ${ℝ}^3$. Use a theorem from this section to shorten your work.]