Spin of a particle (Quantum Mechanics)

Question

1. Why the intrinsic spin cannot be expressed in terms of polar vectors or the orbital variables $\bf r$ and $\bf p$?

2. Or, why do we need matrix representation for Spin?

Answer 1

Spin is an intrinsic quantity of a particle similar to a particle's mass or charge, and has units of angular momentum. It is an observable, and the corresponding operator has a matrix representation with respect to a particular basis.