Chapter 1.7, Problem 13E

The vectors listed in Eq. (10) are used in several of the exercise that follow.

${\mathbf{v}}_1=\left[\begin{array}{c}1\\ 2\end{array}\right],$	${\mathbf{v}}_2=\left[\begin{array}{c}2\\ 3\end{array}\right]$,	${\mathbf{v}}_3=\left[\begin{array}{c}2\\ 4\end{array}\right]$,
${\mathbf{v}}_4=\left[\begin{array}{c}1\\ 1\end{array}\right]$,	${\mathbf{v}}_5=\left[\begin{array}{c}3\\ 6\end{array}\right]$,
${\mathbf{u}}_0=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$,	${\mathbf{u}}_1=\left[\begin{array}{c}1\\ 2\\ -1\end{array}\right]$,	${\mathbf{u}}_2=\left[\begin{array}{c}2\\ 1\\ -3\end{array}\right]$,
${\mathbf{u}}_3=\left[\begin{array}{c}-1\\ 4\\ 3\end{array}\right]$,	${\mathbf{u}}_4=\left[\begin{array}{c}4\\ 4\\ 0\end{array}\right]$,	${\mathbf{u}}_5=\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right]$

In Exercises 1-14, use Eq.(6) to determine whether the given set of vectors is linearly independent or linearly dependent. If the set is linearly dependent, express one vector as a linear combination of the others.

$\left\{{\mathbf{u}}_0,{\mathbf{u}}_1,\mathit{ }{\mathbf{u}}_2,{\mathbf{u}}_4\mathit{ }\right\}$