stunner5000pt
- 1,447
- 5
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 the 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!
[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 the 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!