## One period model Fincial Market - Arbitrage

Hi

Can you help me with the following, i think it is pretty easy but I don't get it:

Consider a discrete one period model of the financial market. We have a risk-free bond and a stock. The bond hast at time 0 a value of 1 and at time 1 $1+r$, , $r>-1$, the stock has at time 0 a value of 3 and with positive probability one of the three values (3 possible states) $\omega_1=1, \omega_2=2, \omega_3=3$. so we have the following equation system:
$
\begin{pmatrix}1 & 1 &1 \\ 1& 2 &3\end{pmatrix}\bold{x}=\begin{pmatrix}\frac{1}{1+ r}\\3\end{pmatrix}$

The question is to determine all interest rates $r$ for which there is no arbitrage and to give an arbitrage opportunity for one of the other $r$.

In a one-period model, I normally look at the equation sytem and determine if we have a unique solution, but how can this be done in this example?

Thank you