quiz_04sle_gaussseidal - Multiple-Choice Test Chapter 04.08...

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04.08.1 Multiple-Choice Test Chapter 04.08 Gauss-Seidel Method 1. A square matrix [ ] n n A × is diagonally dominant if (A) , 1 = n j i j ij ii a a n i ,..., 2 , 1 = (B) , 1 = n j i j ij ii a a n i ,..., 2 , 1 = and , 1 = > n j i j ij ii a a for any n i ,..., 2 , 1 = (C) , 1 = n j ij ii a a n i ,..., 2 , 1 = and , 1 = > n j ij ii a a for any n i ,..., 2 , 1 = (D) , 1 = n j ij ii a a n i ,..., 2 , 1 = 2. Using ] 5 , 3 , 1 [ ] , , [ 3 2 1 = x x x as the initial guess, the values of ] , , [ 3 2 1 x x x after three iterations in the Gauss-Seidel method for = 6 5 2 11 7 2 1 5 1 3 7 12 3 2 1 x x x are
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04.08.2 Chapter 04.08 04.08.2 3. To ensure that the following system of equations, 17 2 5 7 5 2 6 11 7 2 3 2 1 3 2 1 3 2 1 = + + = + + = + x x x x x x x x x converges using the Gauss-Seidel method, one can rewrite the above equations as follows: (A) = 17 5 6 2 5 7 1 2 1 11 7 2 3 2 1 x x x (B) = 6 5 17 11 7 2 1 2 1 2 5 7 3 2 1 x x x (C) = 17 5 6 11 7 2 1 2 1 2 5 7 3 2 1 x x x (D) The equations cannot be rewritten in a form to ensure convergence.
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