Hill Cipher question Recently, I was given three ciphers to crack for my cryptography class. At this point, I have guessed that one of them is likely a Hill cipher (probably 3x3, as that is the most complex we have done so far). 

I have made a fairly good guess of two options for the first seven characters in the cipher, but I found myself unable to figure out the key matrix. So far, I have $\bigl(\begin{smallmatrix}
a&amp;b&amp;c\\ d&amp;e&amp;f\\ g&amp;h&amp;i
\end{smallmatrix} \bigr)$ x $\bigl(\begin{smallmatrix}
14\\ 13\\ 0
\end{smallmatrix} \bigr)$ = $\bigl(\begin{smallmatrix}
10\\ 4\\ 12
\end{smallmatrix} \bigr)$, but since the matrix is modulo 26 there could technically be infinite values for variables a-i (for instance, $14a + 13b + 0c = 10$ could actually be 35, 60, etc.). Is there something that I'm missing?
You would need (at least) 3 pairs of vectors in order to determine the 3*3 matrix.