Given that A $=[-1,0,0,0,0,0,0,0,1,0,0,0,-1,-1$ ; $0,-1,0,0,0,0,0,0,0,1,0,0,-1,0$; $0,0,-1,0,0,0,0,0,0,0,1,0,1,-1$ ; $0,0,0,-1,0,0,0,0,0,0,0,1,0,1$ ; $1,0,0,0,-1,0,0,0,-1,0,0,0,0,0$; $0,1,0,0,0,-1,0,0,0,-1,0,0,0,0$; $0,0,1,0,0,0,-1,0,0,0,-1,0,0,0$; $0,0,0,1,0,0,0,-1,0,0,0,-1,0,0$; $0,0,0,0,0,0,0,0,-0\mathrm{.}9,0,0,0,1,1$; $0,0,0,0,0,1,0,0,0,-1,0,0,0,0$; $0,0,0\mathrm{.}85,0,0,0,0,0,0,0,-1,0,0,0$; $0,0,0,-0\mathrm{.}65,0,0,0,0,0,0,0,1,0,0$; $0\mathrm{.}1,0,0,0,-1,0,0,0,0,0,0,0,0,0$; $0,0,0,0,0,0,0,0,0,0,0,0,-0\mathrm{.}3,0\mathrm{.}7]$;

and

B $=[-10$ ; $-20$ ; $0$; $0$; $0$; $0$; $0$; $0$; $9$; $0$; $0$; $0$; $0$; $0]$;

Where Ax $=$ B :

$-$ write a MATLAB, user$-$defined function that will solve the set of equations using the Gauss Seidel method. Compare how this performs against the results generated using MATLAB's in$-$built functions.

$-$Test your MATLAB code to study the range of possible solutions, i$.$e$.$ solutions for which realistic solutions are possible $($for example, negative flowrates can be solutions, but are not possible$).$

$-$ Try and expand your MATLAB code to develop a code that would handle a more complicate Flowsheet balance $-($ each unknown in the balance represents an unknown ffrom a process flow diagram ie edit amount of inputs, unknowns etc$)($arbitrary number of reactions $,$ for example, or additional units of equipment$).$