Question: how to write system of linear equations in matrix

This question is related to the Question how to find values on internal nodes of mesh

hi friends i have already asked help related to this code which am gona post but this time I am facing some different problem. In the worksheet which i attached below is having algorthim for cubic spline on heat equation. IN this sheet FD equation is my main equation and i want this equation to use boundary conditions mention in code. After using that i want this equation to generate system of linear equations when i=0..M, j=1..N. But i dont want to solve it completely. After this i want that system of linear equations to subsitute values of U[i,j] directly into matrix. Inshort i want matrix of FD equation with utilized boundary conditions. I have tried uptill system of linear equations but have no idea what to do further and how to write that linear equations in 

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