A graph $G$ has an adjacency matrix $A$. If $A^k_{ij}$ represents the number of walks of length $k$ between vertex $i$ and $j$, how many walks of length 3 exist between vertices 1 and 2 if the first row of $A$ is $(0, 1, 1, 0)$ and the second row is $(1, 0, 0, 1)$?