Answer
$\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}$ does not form a basis for $R^2$.
Work Step by Step
From the figure, one can see that the set $\mathbf{v}_{1}=(1,1), \mathbf{v}_{2}=(2,2)$. It is easy to see that $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}$ are linearly dependent. Hence $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}$ does not form a basis for $R^2$.
