Apply Jacobi’s method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each variable. In each case, compare your answer with the exact solution found using any direct method you like.

3x₁ - x₂                  = 1
x₁ + 4x₂ + x₃          = 1
x₂ + 3x₃                 = 1