# Easy linear algebra question

1. Dec 5, 2005

### 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!

2. Dec 8, 2005

### CarlB

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

Carl

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