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Solve the given system of linear equations using the LU Decomposition Method. 2.)    x1 - 2x2 + 5x3  = -7         -2x1 - 3x2 + 4x3 = -14         -3x1 + 5x2 -2x3 = -7

Solve the given system of linear equations using the LU Decomposition Method. 2.)    x1 - 2x2 + 5x3  = -7         -2x1 - 3x2 + 4x3 = -14         -3x1 + 5x2 -2x3 = -7

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 given system of linear equations using the LU Decomposition Method.

2.)    x1 - 2x2 + 5x3  = -7

        -2x1 - 3x2 + 4x3 = -14

        -3x1 + 5x2 -2x3 = -7

These is the example or guide that might help to solve the LUdecomposition method.

 

 

し、U40 ) Laiun + Lau3 し Lしntしてい)しゅ しッUゅ+ Lyz UょットL Ln *A [L][U] LL U2 2. 31 -2 Ly LoiUithz LoiUig + Lゅzu2るtしgc (2)(-%)+L22=3 L22 1/ (2) (a)+ ("/)+U23=1 )(%) +レ2=1 (3) ()+ (2)(Yu) + Lg3=-2 しっろこー35/ L32=2 U.2 U3 , U: U23 L21 L22 0 -La L32 La * A =[L) [U] 3 0 2 3 0 3 2 -3% I 3 /3 3 -1 2 3 う」 -2 0 0 * Ly : BĐ Ux -y 3 0 3y,toyat0y, =1 Y. 3 2 -35/1 Ux -Y "o- 人 X2 メ。: Ox, + x2 + C Yn) 3: 1% 2: 1 Ox, +Ox2 + Xig= -1
Transcribed Image Text:し、U40 ) Laiun + Lau3 し Lしntしてい)しゅ しッUゅ+ Lyz UょットL Ln *A [L][U] LL U2 2. 31 -2 Ly LoiUithz LoiUig + Lゅzu2るtしgc (2)(-%)+L22=3 L22 1/ (2) (a)+ ("/)+U23=1 )(%) +レ2=1 (3) ()+ (2)(Yu) + Lg3=-2 しっろこー35/ L32=2 U.2 U3 , U: U23 L21 L22 0 -La L32 La * A =[L) [U] 3 0 2 3 0 3 2 -3% I 3 /3 3 -1 2 3 う」 -2 0 0 * Ly : BĐ Ux -y 3 0 3y,toyat0y, =1 Y. 3 2 -35/1 Ux -Y "o- 人 X2 メ。: Ox, + x2 + C Yn) 3: 1% 2: 1 Ox, +Ox2 + Xig= -1
Direct Method 2 Decomposition Working Rule : Concider the system of quations Oux ayta, 2 bs In Matrix form AxB whwe, by Decompose the coefficient matrix A into the producte of lower ond upper triomubr matrices wtth diogoral elements in upper tritureular meatrix as unity In Matrix form: A: CL][U] 107 L. I Ui2 u13 wheve, L: U23 L22 Exmeie : Solve the following equations using LU Decompposition method. 3x, - x, x, = 1 2x, + 3x2 + X, :4 3x, + x2 - 2x3:6 Solution: うx, - メ2+メ,: 2x, +3 X2 + X : 4 3x,+メュ2メン X,: ? -1 *A = -2 *A = [L] [U] Lu L22 o U: 0 1 U23 し Crauts Method a, aiz a3 ら、 biz b2i bzz b2n
Transcribed Image Text:Direct Method 2 Decomposition Working Rule : Concider the system of quations Oux ayta, 2 bs In Matrix form AxB whwe, by Decompose the coefficient matrix A into the producte of lower ond upper triomubr matrices wtth diogoral elements in upper tritureular meatrix as unity In Matrix form: A: CL][U] 107 L. I Ui2 u13 wheve, L: U23 L22 Exmeie : Solve the following equations using LU Decompposition method. 3x, - x, x, = 1 2x, + 3x2 + X, :4 3x, + x2 - 2x3:6 Solution: うx, - メ2+メ,: 2x, +3 X2 + X : 4 3x,+メュ2メン X,: ? -1 *A = -2 *A = [L] [U] Lu L22 o U: 0 1 U23 し Crauts Method a, aiz a3 ら、 biz b2i bzz b2n
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