# Basis and Dimension

Let V be the set of all vectors of form $(a, b, c)$ where $a + 2b − c = 0$. Find a basis $B$ for $V$ and find $\dim(V)$.

I'm stuck on this one. I know it won't have dimension of 3 because it's easy to see that it won't span all of $\mathbb{R^3}$

• Have you tried expressing one of $a$,$b$,$c$ in terms of the other two? – Michael M Nov 12 '14 at 0:36

Hint: $(a,b,c) = (a,b,a+2b) = a(1,0,1) + b(0,1,2)$.