1. Consider the linear system \left\{\begin{aligned} x_{1}+4 x_{2} &=0 \\ 4 x_{1}+x_{2} &=0 \end{aligned}\right. The true solution is x1 = -1/15, x2 = 4/15. Apply the Jacobi and Gauss-Seidel methods

with x0 = [0,0]" to the system and find out which methods diverge more rapidly. Next,interchange the two equations to write the system as \left\{\begin{aligned} 4 x_{1}+x_{2} &=0 \\ x_{1}+4 x_{2} &=0 \end{aligned}\right. and apply both methods with x(0) = [0, 0]". Iterate until ||r – x(k)|| < 10-5. Which method converge faster?