Chapter 3.SE, Problem 6SE

$6.$ Let $S=\left\{v_1,v_2,v_3\right\}$, where

$v_1=\left[\begin{array}{c}1\\ -1\\ 1\end{array}\right]$, $v_2=\left[\begin{array}{c}1\\ 2\\ -1\end{array}\right]$, and

$v_3=\left[\begin{array}{c}3\\ 3\\ -1\end{array}\right]$.

$a)$ Find a subset of $S$ that is a basis for $\text{Sp}\left(S\right)$.

$b)$ Find a subset of $S$ that is a basis for $\text{Sp}\left(S\right)$ by setting $A=\left[\begin{array}{ccc}{v}_1& v_2& v_3\end{array}\right]$ and reducing $A^T$ to echelon form.

$c)$ Give an algebraic specification for $\text{Sp}\left(S\right)$, and use that specification to obtain a basis for $\text{Sp}\left(S\right)$.