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SYSTEM I ITERATIVE METHODS ARE USUALLY USED FOR VERY LARGE LINEAR SYSTEMS WITH IMPORTANT APPLICATIONS. THEREFORE, MAKING SURE THAT THE SYSTEM WILL CONVERGE TO THE CORRECT ANSWER IS CRITICAL. KNOWING THIS, CHOOSE THE CORRECT OPTION BELOW: CHOOSE AN OPTION: 2х + бу %3D 3.4 + 8y SYSTEM I. A) SYSTEM I HAS A COEFFICIENT MATRIX S.D.D, SO WE CAN = 2.45 GUARANTEE ITS RESOLUTION THROUGH ITERATIVE METHODS. SYSTEM II x + 2y + z = 12 B) SYSTEM II IS THE ONLY ONE THAT HAS A COEFFICIENT Зу + 52 y + 3z = 10 MATRIX S.D.D., SO IT IS THE ONLY ONE WITH GUARANTEED = / 2х CONVERGENCE. C) ALTHOUGH NONE OF THE THREE COEFFICIENT MATRICES IS S.D.D., WE CANNOT GUARANTEE DIVERGENCE IN THE SYSTEM II 2x, + 3x2 + x; + X4 = 2 APPLICATION OF ITERATIVE METHODS. 4x, + 7x, + 4x, + 3x, = 1 6x, + 9x, + 9x, + &x, 4x, + 7x, + 6x; + 4x4 = 3 D) WE CAN GUARANTEE THE CONVERGENCE OF THE THREE = 2 SYSTEMS. STRICTLY DIAGONALLY DOMINANT E) WE CAN GUARANTEE THAT NONE OF THE SYSTEM CONVERGES. = S.D.D

SYSTEM I ITERATIVE METHODS ARE USUALLY USED FOR VERY LARGE LINEAR SYSTEMS WITH IMPORTANT APPLICATIONS. THEREFORE, MAKING SURE THAT THE SYSTEM WILL CONVERGE TO THE CORRECT ANSWER IS CRITICAL. KNOWING THIS, CHOOSE THE CORRECT OPTION BELOW: CHOOSE AN OPTION: 2х + бу %3D 3.4 + 8y SYSTEM I. A) SYSTEM I HAS A COEFFICIENT MATRIX S.D.D, SO WE CAN = 2.45 GUARANTEE ITS RESOLUTION THROUGH ITERATIVE METHODS. SYSTEM II x + 2y + z = 12 B) SYSTEM II IS THE ONLY ONE THAT HAS A COEFFICIENT Зу + 52 y + 3z = 10 MATRIX S.D.D., SO IT IS THE ONLY ONE WITH GUARANTEED = / 2х CONVERGENCE. C) ALTHOUGH NONE OF THE THREE COEFFICIENT MATRICES IS S.D.D., WE CANNOT GUARANTEE DIVERGENCE IN THE SYSTEM II 2x, + 3x2 + x; + X4 = 2 APPLICATION OF ITERATIVE METHODS. 4x, + 7x, + 4x, + 3x, = 1 6x, + 9x, + 9x, + &x, 4x, + 7x, + 6x; + 4x4 = 3 D) WE CAN GUARANTEE THE CONVERGENCE OF THE THREE = 2 SYSTEMS. STRICTLY DIAGONALLY DOMINANT E) WE CAN GUARANTEE THAT NONE OF THE SYSTEM CONVERGES. = S.D.D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5 ITERATIVE METHODS ARE USUALLY USED FOR VERY LARGE LINEAR SYSTEMS WITH IMPORTANT APPLICATIONS. THEREFORE, MAKING SURE THAT THE SYSTEM WILL CONVERGE TO THE CORRECT ANSWER IS CRITICAL. KNOWING THIS, CHOOSE THE CORRECT OPTION BELOW: CHOOSE AN OPTION: SYSTEM I. 2х + бу 3.4 %3D A) SYSTEM I HAS A COEFFICIENT MATRIX S.D.D, SO WE CAN |x + 8y = 2.45 GUARANTEE ITS RESOLUTION THROUGH ITERATIVE METHODS. SYSTEM II x + 2y + z = 12 Зу + 52 3D 1 B) SYSTEM II IS THE ONLY ONE THAT HAS A COEFFICIENT x - MATRIX S.D.D., SO IT IS THE ONLY ONE WITH GUARANTEED 2x y + 3z = 10 CONVERGENCE. C) ALTHOUGH NONE OF THE THREE COEFFICIENT MATRICES IS S.D.D., WE CANNOT GUARANTEE DIVERGENCE IN THE SYSTEM III 2x, + 3x, + x; + X4 = 2 APPLICATION OF ITERATIVE METHODS. 4x, + 7x, + 4x ; + 3x, 6x, + 9x, + 9x; + &x, 4х, + 7x, + бх, + 4x, %3D 2 = 1 = 3 D) WE CAN GUARANTEE THE CONVERGENCE OF THE THREE SYSTEMS. STRICTLY DIAGONALLY DOMINANT E) WE CAN GUARANTEE THAT NONE OF THE SYSTEM = S.D.D CONVERGES.
Transcribed Image Text:5 ITERATIVE METHODS ARE USUALLY USED FOR VERY LARGE LINEAR SYSTEMS WITH IMPORTANT APPLICATIONS. THEREFORE, MAKING SURE THAT THE SYSTEM WILL CONVERGE TO THE CORRECT ANSWER IS CRITICAL. KNOWING THIS, CHOOSE THE CORRECT OPTION BELOW: CHOOSE AN OPTION: SYSTEM I. 2х + бу 3.4 %3D A) SYSTEM I HAS A COEFFICIENT MATRIX S.D.D, SO WE CAN |x + 8y = 2.45 GUARANTEE ITS RESOLUTION THROUGH ITERATIVE METHODS. SYSTEM II x + 2y + z = 12 Зу + 52 3D 1 B) SYSTEM II IS THE ONLY ONE THAT HAS A COEFFICIENT x - MATRIX S.D.D., SO IT IS THE ONLY ONE WITH GUARANTEED 2x y + 3z = 10 CONVERGENCE. C) ALTHOUGH NONE OF THE THREE COEFFICIENT MATRICES IS S.D.D., WE CANNOT GUARANTEE DIVERGENCE IN THE SYSTEM III 2x, + 3x, + x; + X4 = 2 APPLICATION OF ITERATIVE METHODS. 4x, + 7x, + 4x ; + 3x, 6x, + 9x, + 9x; + &x, 4х, + 7x, + бх, + 4x, %3D 2 = 1 = 3 D) WE CAN GUARANTEE THE CONVERGENCE OF THE THREE SYSTEMS. STRICTLY DIAGONALLY DOMINANT E) WE CAN GUARANTEE THAT NONE OF THE SYSTEM = S.D.D CONVERGES.
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