Easy linear algebra question


by stunner5000pt
Tags: algebra, linear
stunner5000pt
stunner5000pt is offline
#1
Dec5-05, 07:27 PM
P: 1,445
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}{c|ccc}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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CarlB
CarlB is offline
#2
Dec8-05, 03:55 AM
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P: 1,204
Your calculation of the eigenvalues is in error (at least). For example, (1,0,-1) has eigenvalue of 2.

Carl


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