Why do different methods for solving Xc=y in python give different solution when they should not?

Question

I was trying to solve a linear system Xc=y that was square. The methods I know to solve this are:

1. using inverse c=

Answer 1

The issue is floating point accuracy. You're raising numbers between zero and one to the 30th power, then adding them together. If you were doing this with infinite precision arithmetic, the methods would recover the inputs. With floating point arithmetic, precision loss means you can't.