What is the real-valued function M used in the algorithm's pseudo-code? And what is the set-valued function I? I guess that I(v) is either the set of edges connected to v or not connected to v. I have no guess for M.

@rockyicer As you likely realize, what you're currently asking about has nothing to do with the mathematical aspects of the solution. Rather, I did it solely for the display aspect, to put the variables back the way that you originally had them.

Before I give a more-thorough Answer, tell me which (if any) of these Maple commands you already have a basic understanding of: type, indets, subsindets, cat, op, op(0, ...).

In my command above, patindex(anything) is the type of subexpression to be changed. The pat stands for "patterned" (which I think you figured out already). So, it looks for indexed expressions with a certain type pattern in the indices. But, since I specifed anything, it'll match any indexed expression. So, I could've (and for sake of simplicity, I should've) used indexed instead of patindex(anything). See the help pages ?type, ?type,structure (for patindex), ?type,anything, ?indexed, ?type,indexed.

Supposed that n is an indexed name, for example n = x[1,2]. Then op(0, n) = x, op(n) = (1, 2), and op(0.., n) = (x, 1, 2). (There's a distinction between indexed and subscripted. Subscripted refers to the form of typographic display of an expression, but indexed refers to its internally stored structure.) The op stands for "operands". It's the most-fundamental Maple command for deconstructing expressions. See ?op and ?name.

The cat stands for "catenate". It's the Maple command for building symbols and strings. So, using the same n as above, the cat command becomes cat(x, (1, 2)) ==> cat(x, 1, 2) ==> x12. See ?cat.

Regarding the length and complexity of my command: It could be replaced with

S:= simplify(solve(Eqs, Svars));  #Do the algebra.
subsindets[2](S, indexed, 0.., cat@op);  #Do the typography.

The [2] after subsindets causes the indexed subexpressions to be passed as the 2^nd argument to the transformer, cat@op, with 0.. being its (constant) 1^st argument. See ?subsindets.

@nm You're right about the right directional limit, but I have some doubt left about the left: limit(ln(x)/x, x= 0, left) returns infinity. I expected (1 - I)*infinity.

@bstuan Part b is false. The simplest counterexample that I can come up with is 

A = [ 0  1 ]
    [ 0  0 ]

B = [-1  0 ]
    [-1 -1 ]

The complaint that you get from MaplePrimes is advisory, not prohibitive. In the case of Maple Flow, there's no other convenient way to post your work, so just ignore the complaint and post images anyway.

@acer The fact that dsolve is shown to run without error with option arbitraryconstants= subscripted indicates that the OP is using a quite-recent version of Physics updates.

@rockyicer Good job, and thank you. Yes, I had guessed that including equ6 and using your original equ5 would give it enough information to eliminate f0, but I didn't explore that. I'm glad that you did.

A few hints for part a:

1. A square matrix A such that A^k = 0 for some positive integer k is called nilpotent. You should be able to find some useful details about nilpotent matrices by web searching.
2. There's nothing special about 2023 here; any positive integer will do. In other words, if A is nilpotent, then I - A is invertible.
3. Using the distributive property of matrix multiplication, simplify (by hand, not by Maple) 
   (I - A).(I + Sum(A^k, k= 1..2022)). 

@mmcdara Before one proceeds too far along the lines that you suggest (file transfer, etc.), it should be pointed out that Maple has had a built-in Python interpreter since Maple 2018. I know that you use Maple 2015 and may not be aware of this.

See help page ?Python.

@mmcdara Thanks, I voted up for yours also.

I just made a very small modification to my Answer to have Ia1 expressed in terms of Va1 per the OP's request. The modifcation is to subtract Va1 from the Svars. 

What makes you think that they can't be solved by Maple? Don't you think that it's more likely that it's you, not Maple, doing something wrong?

@jediknight Don't despair: I'm sure that it's possible with Maple V. I used it extensively when it was the current version, and I made many plots far more complicated than this. Try this:

semilogplot(
    map(q-> subs(Q= q, a), Qs), wx= 0.2..2,
    thickness= 5, axes= boxed, labels= [w, Gain], title= `Gain(w, Q, m)` 
);

The wx= 0.2..2 is an essential part of the command. The remaining plot options (from thickness to title) can be omitted until we get the basic plot correct. 

@jediknight You've used extra parentheses that weren't in my command. Also, you've changed plots to plot. It's the extra parentheses that are the direct cause of the error shown. They change the numbers of arguments (which the error message erroneously calls "parameters") of the seq from 2 to 1. 

@jediknight Please upload a worksheet (*.mws) showing the code execution from restart to the latest error.

@jediknight Try this:

plots[semilogplot](
    [seq](subs(Q= Qs[k], a), k= 1..nops(Qs)), wx= 0.2..2, thickness= 5,
    axes= boxed, labels= [w, Gain], title= `Gain(w, Q, m)` 
);