Let $\displaystyle v_1=\begin{bmatrix}1 \\ 1 \\ a\end{bmatrix},v_2=\begin{bmatrix}1 \\ a \\ 1\end{bmatrix},$ and $\displaystyle v_3=\begin{bmatrix}a \\ 1 \\ 1\end{bmatrix}$

For which values of the parameter a is $\displaystyle v_1$,$\displaystyle v_2$ and $\displaystyle v_3$ a basis for $\displaystyle R^3$?