Power System Analysis: Node Elimination Explained

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Preface: I am an electrical engineer studying for the PE exam. I am reviewing power system analysis and have come across something I do not remember in any of my classes.

I'll not bore you with the entire problem. Suffice it to say there is a 4x4 matrix that is being partitioned as follows:

[-9.8, 0.0, 4.0 | 5.0]
[0.0, -8.3, 2.5 | 5.0]
[4.0, 2.5, -14.5 | 8.0]
---------------------
[5.0, 5.0, 8.0, | -18.0]

Sorry for the weird formatting.

Now according to my book, "Elements of Power System Analysis" by Stevenson, I need to eliminate node 4 (the bottom row and last column). For ease of understanding I will use subscripts so that element in row 2 column 3 is E23.

I'm not sure how to explain this so let me show you.

the new matrix will be 3x3 and will be constructed thusly:

E11(new matrix) = E11 - (E14xE41)/E44 = -9.8 - (5x5)/-18 = -8.411
E32(new matrix) = E32 - (E34xE42)/E44 = 2.5 - (8x5)/-18 = 4.722

Each element of the new matrix is constructed the same way yielding:

[-8.411, 1.389, 6.222]
[1.389, -6.911, 4.722]
[6.222, 4.722, -10.944]

Now the question.

First, how do I know if I can eliminate a particular row? Is there some method like the inverted matrix has a particular form, or something?

Can anyone help me understand WHEN I can apply this method?

Thanks.
 
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I can follow you up until your Question, but from there on it is unclear what you want to know.

What row from what matrix do you want to eliminate?
 
No, I know whuch one was removed, I just have no idea why THAT row was removed.

If I had a matrix that was not in my textbook, how am I to know which row is to be removed if, indeed, any row CAN be removed? I don't understand how I would know WHEN I can apply this method.

I also don't really understand WHY this method even works.
 

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