Solve the given system of linear equations using the LU Decomposition Method.3) 3x1 + 4x2 + 2x3 = 15 5x1 + 2x2 + x3 = 10 2x1 + 3x2 + 2x3 = 10These is the example or guide of LU decomposition method that might help.... し、U40 )Laiun + Lau3し Lしntしてい)しゅしッUゅ+ Lyz UょットLLn*A [L][U]LL U22.31 -2Ly LoiUithz LoiUig + Lゅzu2るtしgc(2)(-%)+L22=3L22 1/(2) (a)+ ("/)+U23=1)(%) +レ2=1(3) ()+ (2)(Yu) + Lg3=-2しっろこー35/L32=2U.2 U3, U:U23L21 L22 0-La L32 La* A =[L) [U]3 02 3 03 2 -3%I 3 /33 -12 3う」-20 0* Ly : BĐ Ux -y3 03y,toyat0y, =1Y.3 2 -35/1Ux -Y"o- 人X2メ。:Ox, + x2 + C Yn) 3: 1% 2: 1Ox, +Ox2 + Xig= -1 Direct Method 2 DecompositionWorking Rule : Concider the system of quationsOux ayta, 2 bsIn Matrix form AxBwhwe,byDecompose the coefficient matrix A into theproducte of lower ond upper triomubr matriceswtth diogoral elements in upper tritureular meatrixas unityIn Matrix form: A: CL][U]107L.I Ui2 u13wheve, L:U23L22Exmeie :Solve the following equations using LU Decomppositionmethod.3x, - x, x, = 12x, + 3x2 + X, :43x, + x2 - 2x3:6Solution:うx, - メ2+メ,:2x, +3 X2 + X : 43x,+メュ2メンX,: ?-1*A =-2*A = [L] [U]Lu L22 oU: 0 1 U23しCrauts Methoda, aiz a3ら、 bizb2i bzz b2n

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Solve the given system of linear equations using the LU Decomposition Method. 3) 3x1 + 4x2 + 2x3 = 15 5x1 + 2x2 + x3 = 10 2x1 + 3x2 + 2x3 = 10 These is the example or guide of LU decomposition method that might help

Solve the given system of linear equations using the LU Decomposition Method. 3) 3x1 + 4x2 + 2x3 = 15 5x1 + 2x2 + x3 = 10 2x1 + 3x2 + 2x3 = 10 These is the example or guide of LU decomposition method that might help

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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Question

Solve the given system of linear equations using the LU Decomposition Method.

3) 3x₁ + 4x₂ + 2x₃ = 15

5x₁ + 2x₂ + x₃= 10

2x₁+ 3x₂ + 2x₃ = 10

These is the example or guide of LU decomposition method that might help....

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

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