Given the system: $-x_1 - x_2 + 5x_3 = 3$ $-x_1 + 4x_2 - x_3 = 2$ $8x_1 - x_2 - x_3 = 6$ Rearrange the system (if possible, to grantee the convergence), and then use Gauss Seidel method to obtain an approximate solution.
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$$x_1 = -x_2 + 5x_3 + 3$$ $$x_2 = \frac{1}{4}x_1 + \frac{1}{4}x_3 - \frac{1}{2}$$ $$x_3 = 8x_1 - x_2 - 6$$ Show more…
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Use the Gauss-Seidel method to solve the following system until the percent relative error falls below es = 5%. Before solving, change the order of equations to satisfy |aii| > ∑ |aij| -3x1 - 6x2 + 2x3 = -61.5 10x1 + 2x2 - x3 = 27 x1 + x2 + 5x3 = -21.5 Apply relaxation ̀λ = 1.2 in your solution. 2. [0.8 -0.4 0; -0.4 0.8 -0.4; 0 -0.4 0.8] {x1; x2; x3} = {41; 25; 105} Take the Inverse of Matrix by LU decomposition using Thomas algorithm, and solve this system by using Inverse Matrix.
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