Chapter 3.5, Problem 3E

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 I-6, determine by inspection why the given set $S$ is not a basis for $R^2$. (That is, either $S$ is linearly dependent or $S$ does not span $R^2$.)

$S=\left\{{\text{u}}_1{\text{, u}}_2,{\text{u}}_3\right\}$