Repeat the given exercise using the GaussSeidel method. 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. Compare the number of iterations required by the Jacobi and Gauss-Seidel methods to reach such an approximate solution.

3x₁ - x₂                 = 1
-x₁ + 3x₂ - x₃        = 0
-x₂ + 3x₃ -  x₄       = 1

-x₃ + 3x₄              = 1