What is the Spectral Radius of the Gauss-Seidel Method for this Matrix?

[stunner5000pt]

given this matrix
$$x_{1} + 2 x_{2} - 2x_{3} =7$$
$$x_{1} + x_{2} + x_{3} =2$$
$$2x_{1} + 2x_{2} + x_{3} =5$$

Show taht $\rho(T_{g}) = 2$ where rho represenets the spectral radius for this matrix
Tg represents the matrix formed from teh Gauss Seidel method

i found Tg to be like this
$$\left(\begin{array}{c|ccc}0&-2&-2&7\\-1&0&-1&2\\-2&-2&0&5\end{array}\right)$$

the Matrix Tg in question is
$$\left(\begin{array}{ccc}0&-2&-2\\-1&0&-1\\-2&-2&0\end{array}\right)$$


spectral radius is the maximum of the eigenvalues. But for this matrix the eigenvalues i obtained were all zero. (Am i wrong here, do you wnat me to show the working?)
So how can the spectral radius be 2??

Please help! Your help is greatly appreciated!

 

[CarlB]

Your calculation of the eigenvalues is in error (at least). For example, (1,0,-1) has eigenvalue of 2.

Carl