Find all values a for which $\displaystyle \begin{bmatrix}1 \\ 1 \\ 1\end{bmatrix}$ is in the span of $\displaystyle v_1,v_2,v_3$. Also find the values of a for which $\displaystyle v_1,v_2,v_3$ are linearly independent.

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

When I try to do rref I get all zeros in the bottom...