I have a set of vectors:
$$V=\lbrace x\in\Bbb{R}^5:x_1+x_2+x_3+x_4+x_5=0\rbrace$$
I need to find basis for this set of vectors. What is the "algorithm" for solving such problems? Where should I start?
EDIT:
Is this a valid basis: $\lbrace[1,0,0,0,-1]^T,[0,1,0,0,-1]^T,[0,0,1,0,-1]^T,[0,0,0,1,-1]^T\rbrace$?