Solving a given set of linear equations, without using any numeric python library
First determines the following conditions;
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If 𝑟𝑎𝑛𝑘(𝐴) = 𝑛, then it finds the unique solution and additionally, it also finds 𝐴^−1.
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If 𝑟𝑎𝑛𝑘(𝐴) = 𝑟𝑎𝑛𝑘(𝐴|𝑏) < 𝑛, then it gives an arbitrary solution.
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If 𝑟𝑎𝑛𝑘(𝐴) < 𝑟𝑎𝑛𝑘(𝐴|𝑏), then it only states that the problem has no solution at all.
The first number in .txt files gives the number 𝑛. Then, there is a 𝑛 x (𝑛 + 1) matrix which represents the augmented matrix [𝐴|𝑏].