The Gauss-Seidel method diverges if we start the process with initial values of zero. No other starting point has been provided. Start by letting all variables=0. We use these and the equations below to derive subsequent iterations of the variables.
I₁=(7I₃-3I₂)/5, (I₁)₁=0 from initial conditions and from this equation.
If we continue substituting for each iteration, the values diverge rapidly. Clearly, (0,0,0) is not a good starting point.
The linear equations lead to I₁=1, I₂=3, I₃=2 using other methods.