I have tried to follow what you have set out, but I am struggling with the development of your dependancy matrix. (I would have compiled a matrix based on nodes rather than arcs (joins not arches).
However, assuming you have developed the matrices for the X and Y axis and you simply wish to add and multiply the matrices then Excel has this capability.
If your matrices are square then elemental addition is easy and I suspect you have done this.
Multiplication is achieved using MMult. The help pages are good and explain how the function works. Make sure you use cntrl+shift+enter to create the Array formula.
Hope this helps,