Chapter 4.6, Problem 33P

Let $v_1=\left(1,1\right)$ and $v_2=\left(-1,1\right)$.

(a)	Show that $\left\{v_1,v_2\right\}$ spans ${ℝ}^2$.
(b)	Show that $\left\{v_1,v_2\right\}$ is linearly independent.
(c)	Conclude from (a) or (b) that $\left\{v_1,v_2\right\}$ is a basis for ${ℝ}^2$. What theorem in this section allows you to draw this conclusion from either (a) or (b), without proving both?