Answer 1

Numpy stands for "numeric Python" while Sympy stands for "symbolic Python".

In Numpy, every calculation is numeric. Everything is made for very fast computing.
That's why, for example, Numpy matrices must have a type (as in other languages) and the computations may vary from a type to another.
They are more useful for engineers using very large matrices and making many computations.

On the other hand, everything in Sympy is symbolic. Computing is made using CAS (Computer Algebra System) and results are exact when possible.
Sympy matrices don't need to be typed and may include symbolic variables.
They are more useful for students learning algebra.

I hope it helps.