Given real $\mu \neq 0$, we consider the matrix

$$A=\left[\begin{array}{cccc} \frac{1}{\mu} & 1 & 0 & 0 \\ -1 & \frac{1}{\mu} & 1 & 0 \\ 0 & -1 & \frac{1}{\mu} & 1 \\ 0 & 0 & -1 & \frac{1}{\mu} \end{array}\right]$$

Construct the Jacobi and Gauss-Seidel iteration matrices originating in the solution of the linear system $A x=b$.

Determine the range of real $\mu \neq 0$ for which each iterative procedure converges.