Math Problem, please be original and with clear handwriting, thank you!

1. (25 points) Consider the linear system of PDEs, _. .. _ _ 1 4 ug+Aum0, A[4 1]. i. Show that the system is hyperbolic. ii. Write down the solution for the initial condition u(a:, 0) = [1, O]T when a: 0. iii write down the upwind scheme for this system