Chapter 3.5, Problem 12E

Exercises 1-14 refer to the vectors in (15)

${\text{u}}_{\text{1}}=\left[\begin{array}{c}1\\ 1\end{array}\right]$,	${\text{u}}_{\text{2}}=\left[\begin{array}{c}1\\ 2\end{array}\right]$,	${\text{u}}_{\text{3}}=\left[\begin{array}{c}-1\\ 1\end{array}\right]$,
${\text{u}}_{\text{4}}=\left[\begin{array}{c}0\\ 0\end{array}\right]$,	${\text{u}}_{\text{5}}=\left[\begin{array}{c}3\\ 3\end{array}\right]$,	${\text{v}}_{\text{1}}=\left[\begin{array}{c}1\\ -1\\ 1\end{array}\right]$,
${\text{v}}_{\text{2}}=\left[\begin{array}{c}0\\ 1\\ 2\end{array}\right]$,	${\text{v}}_{\text{3}}=\left[\begin{array}{c}1\\ -1\\ 0\end{array}\right]$,	${\text{v}}_{\text{4}}=\left[\begin{array}{c}-1\\ 3\\ 3\end{array}\right]$

In Exercises 10-14, use Theorem 9, property 3. to determine whether the given set is a basis for the indicated vector space.

$S=\left\{{\text{v}}_1,{\text{v}}_2{\text{, v}}_3\right\}$ for $R^3$.