I was tending to go in your direction, but then the formula contains a division and we could be faced with a division by zero error. Which makes me a bit uncert

I was tending to go in your direction, but then the formula contains a division and we could be faced with a division by zero error. Which makes me a bit uncertain whether it is so simple. If we are guaranteed the matrix is invertible then doing it by hand is something I would prefer. And likely if it is not then as well since... The invertibility issue also plagues any library and while it may not blow up by a division by zero we likely still would need to handle that case. This requires to understand the libraries handling of corner cases and how it affects the results.