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Numerical Method Analysis :

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Solve the following system using Gauss seidal iterative method with initial guess (0, 0, 0) and tolerance 0.001.

$\left\{\begin{matrix} 2x_{1}-3x_{2}+x_{3} = 5\\ x_{1}+4x_{2}+12x_{3} = 10\\ 6x_{1}+x_{2}+5x_{3} = 9 \end{matrix}\right.$
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