I thought choosing the free variable was simple (and it probably is), but I'm having difficulty on this one.

The RREF of the matrix is:

$\displaystyle $\begin{array}{ccccc}

1 & 0 & 0 & \frac{2}{5} & 0\\

0 & 1 & 0 & \frac{-3}{5} & 0\\

0 & 0 & 1 & \frac{-1}{5} & 0\end{array}$$

Now, I thought the free variables were supposed to be those that aren't associated with a leading one in a reduced form of the matrix. However,the answer for this problem has C3 as the free variable. C3 corresponds to a leading one! How is this?