If you are looking for an answer to "How to modify an existing matrix to append new rows/columns?", you can do this as below:
% add a new column to the matrix A
A = [A new_column];
% add a new row to the matrix
A = [A; new_row];
new_row or new_column dimensions should match with the corresponding dimensions of A.
If you looking for an answer to part (c) of the problem, a hint is provided in the question itself. You need to construct a new balance equation and transform it as a new row/column to be added to the existing coefficient matrix "A" and add the new unknown variable from the balance equation to the "x" vector.
