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Easy linear algebra question 
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#1
Dec505, 07:27 PM

P: 1,439

given this matrix
[tex] x_{1} + 2 x_{2}  2x_{3} =7 [/tex] [tex] x_{1} + x_{2} + x_{3} =2 [/tex] [tex] 2x_{1} + 2x_{2} + x_{3} =5 [/tex] Show taht [itex] \rho(T_{g}) = 2 [/itex] 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 [tex] \left(\begin{array}{cccc}0&2&2&7\\1&0&1&2\\2&2&0&5\end{array}\right) [/tex] the Matrix Tg in question is [tex] \left(\begin{array}{ccc}0&2&2\\1&0&1\\2&2&0\end{array}\right) [/tex] 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! 


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