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2x1 + 12 I3 = 0 %D + 13 = 4 T1 + 12 + 13 = 0 %3D

2x1 + 12 I3 = 0 %D + 13 = 4 T1 + 12 + 13 = 0 %3D

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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Solve the following using Gauss elimination: 1. 2x1 + 12 %3D + 13 4 Xị + 12 + 13 2. X2 + 13 1 + 13 1 + 12 3. 12 + 2x1 + 3x2 + 4x3 3 2x2 1 4. 2x2 3x1 + 3x3 -1 %3D X2 + 4 %3D 3x3 = 10 You may need to think carefully about this system. 1. Calculate LU decompositions for each of these matrices 2 1 -4 1 3 2 2 1 (a) A = || (Б) А —D (c) A =| 2 8 5 2 2 -2 -4 -6 6 3-11 1 11 4 2. Using the answers obtained in Question 1, solve the following systems of equations. 2 (a) 1 -4 –6 X2 2 1 -4 (Б) 6 3 -11 2 2 -2 1 3 2 (c) 8 5 %3D 111 4 IL |||| I| || || |L || || I| ||||
Transcribed Image Text:Solve the following using Gauss elimination: 1. 2x1 + 12 %3D + 13 4 Xị + 12 + 13 2. X2 + 13 1 + 13 1 + 12 3. 12 + 2x1 + 3x2 + 4x3 3 2x2 1 4. 2x2 3x1 + 3x3 -1 %3D X2 + 4 %3D 3x3 = 10 You may need to think carefully about this system. 1. Calculate LU decompositions for each of these matrices 2 1 -4 1 3 2 2 1 (a) A = || (Б) А —D (c) A =| 2 8 5 2 2 -2 -4 -6 6 3-11 1 11 4 2. Using the answers obtained in Question 1, solve the following systems of equations. 2 (a) 1 -4 –6 X2 2 1 -4 (Б) 6 3 -11 2 2 -2 1 3 2 (c) 8 5 %3D 111 4 IL |||| I| || || |L || || I| ||||
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