# Easy linear algebra question

by stunner5000pt
Tags: algebra, linear
 P: 1,440 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!