(Solved): 2. Consider the initial value problem (it is a system of equations) \[ \left\{\begin{array} { l } { ...

2. Consider the initial value problem (it is a system of equations) \[ \left\{\begin{array} { l } { x ^ { \prime } = - y , } \\ { y ^ { \prime } = x } \end{array} \text { with } \left\{\begin{array}{l} x(0)=1, \\ y(0)=0 \end{array}\right.\right. \] Use Euler's method to compute the solution and calculate the quantity \( A=\left(x^{n}\right)^{2}+\left(y^{n}\right)^{2} \) where \( \left(x^{n}, y^{n}\right) \) is the solution computed by Euler's method at step \( n \). What is the value of \( A \) for \( n=2 \) when you use a step size \( h=1 \) ? (a) 4 (b) 2 (c) 1 (d) 8