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I have problem with regard to ill-conditioned linear system of solving sets of simultaneous equations using Mathematica program.

I have tried my best to find a way to solve this but none was successful.

From the file attached (mathematica notebook), I got results from m =1 and n =1 until m = 7 and n = 7, i,e. the systems are well-conditioned.

However, the problem started from when m = 9 and n = 9 due to ill-conditioned systems. Note that m = n = 1,3,5,6,7,9,.........99.

Iam trying to find a treatment so that the matrix would not become a singular.

Thanks in advance.

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# Please help me to solve ill-conditioned linear system of matrix

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