biosimulationII hw2

8333 14959 090666 12148 14333 19727 090464 084914

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Unformatted text preview: The algorithm to solve [L][Z]=[C] is given by (A) z1 = c1 / l11 for i from 2 to n do sum = 0 for j from 1 to i do sum = sum + lij * z j end do zi = (ci – sum) / lii end do (B) z1 = c1 / l11 for i from 2 to n do sum = 0 for j from 1 to (i-1) do sum = sum + lij * z j end do zi = (ci – sum) / lii end do (C) z1 = c1 / l11 for i from 2 to n do for j from 1 to (i-1) do sum = sum + lij * z j end do zi = (ci – sum) / lii end do (D) for i from 2 to n do sum = 0 for j from 1 to (i-1) do sum = sum + lij * z j end do zi = (ci – sum) / lii end do 11. A square matrix [A]nxn is diagonally dominant if n (A) aii ≥ ∑ aij , i = 1, 2, …, n j =1 i≠ j n n j =1 i≠ j j =1 i≠ j (B) aii ≥ ∑ aij , i = 1, 2, …, n and aii > ∑ aij , for any i = 1, 2, …, n (C) (D) n n j =1 n j =1 aii ≥ ∑ aij , i = 1, 2, …, n and aii > ∑ aij , for any i = 1, 2, …, n aii ≥ ∑ aij , i = 1, 2, …, n j =1 12. Using [x1 x2 x3] = [1 3 5] as the initial guess, the value of [x1 x2 x3] after three iterations in Gauss-Seidel method for Ⱥ12 7 3 Ⱥ Ⱥ x1 Ⱥ Ⱥ 2Ⱥ Ⱥ 1 5 1 Ⱥ Ⱥ x Ⱥ = Ⱥ− 5Ⱥ Ⱥ Ⱥ Ⱥ 2 Ⱥ Ⱥ Ⱥ Ⱥ 2 7 − 11Ⱥ Ⱥ x3 Ⱥ Ⱥ 6Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ is (A) (B) (C) (D) [-2.8333 [1.4959 [0.90666 [1.2148 -1.4333 -1.9727] -0.90464 -0.84914] -1.0115 -1.0242] -0.72060 -0.82451] 13. To ensure that the following system of equations, 2 x1 + 7 x2 − 11x3 = 6 x1 + 2 x2 + x3 = − 5 7 x1 + 5 x2 + 2 x3 = 17 converges using Gauss-Seidel Method, one can rewrite the above equations...
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This note was uploaded on 08/30/2011 for the course BUSN 1003 taught by Professor Carr,r during the Spring '08 term at Arkansas State.

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