Chapter 3.3, Problem 11E

Exercises $1-11$ refer to the vectors in Eq. $\left(14\right)$.

$a=\left[\begin{array}{c}1\\ -1\end{array}\right]$, $c=\left[\begin{array}{c}-2\\ 2\end{array}\right]$, $e=\left[\begin{array}{c}0\\ 0\end{array}\right]$.

In Exercises $1-11$, either show that $Sp\left(S\right)=R^2$ or give an algebraic specification for $Sp\left(S\right)$. If $Sp\left(S\right)\ne R^2$, then give a geometric description of $Sp\left(S\right)$.

$S=\left\{a,c,e\right\}$.