Let

V={(x$\displaystyle _1$,x$\displaystyle _2$,x$\displaystyle _3$,x$\displaystyle _4$,x$\displaystyle _5$) $\displaystyle \in$R$\displaystyle ^5$: x$\displaystyle _1$-2x$\displaystyle _2$+3x$\displaystyle _3$-x$\displaystyle _4$+2x$\displaystyle _5$=0}.

(a) Show that S={(0,1,1,1,0)} is a linearly independent subset of V.

(b) Extend S to a basis for V.