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Matrix inversion

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I've been tasked with coding a 2d square matrix inversion routine in c/c++. The side of the matrix is expected to be in the range >= 2 and <= 70. My knowledge of numerical algorithms is very limited - but as I wasn't present when the task was handed out I drew by default the short straw as nobody else wanted it either! Please don't ask why or say that matrix inversion is usually not the way to go etc etc etc. I'm not to reason why but to produce or die!

I've looked on the internet and found some C++ code that does the job - but it's O(n!) (yes, n factorial). It works but is obviously slow for larger matrix sizes. Other internet references mention gauss elimination etc etc but this is beyond my maths level for this topic.

Can anyone help with a link to a resource that explains simply how to invert a matrix or - even better - a link to some c/c++ that is efficient for large matrix sizes.

Thanks.

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