Past exam of the mathematical methods I course of the University of Oxford / 2015 resit / 7 / iii / Solution

No. Calling the three vectors $v_1,v_2,v_3$ in order, direct addition gives $v_3=v_1+v_2$. This nontrivial linear dependence prevents them from forming a basis of ${\mathbb{R}}^3$. The first two are not proportional, so the span has dimension two.