The system of four equations (numbered 1 through 4) shown below is to be solved with Gauss_Seidel iteration. (1) 3w - 9x + 4y + z = 10 (2) 2w + 7x - 2y - 8z = -5 (3) 2w - 3x - 5y + z = 12 (4) 6w + x + 4y - 2z = -3 The order of the equations that guarantees convergence is: 1-2-3-4 3-2-4-1 3-1-4-2 3-2-1-4 None of these options will guarantee convergence
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Diagonal dominance means that the absolute value of the diagonal element in each row is greater than the sum of the absolute values of the other elements in the same row. Let's check each option: 1-2-3-4: (1) |3w| > |(-9x) + 4y + 2| (2) |Zx| > |2w - 2y - 8z| (3) Show more…
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