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How to solve an underdetermined system in Mathematica

Hi guys , I have a Mathematica code that i wrote to find the natural frequencies of a triangular plate. The problem that i am facing is when i increase the number of terms above 9, i get an underdetermined system of linear equations.

Any idea how to solve this problem I have attached my code below

Thank you very much in advance Peter

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POSTED BY: peter azizi
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