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

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.

   x1 - 2x2 + 5x3 = -7

 -2x1 - 3x2 + 4x3 = -14

 -3x1 + 5x2 - 2x3 = -7

These is the example or guide of LU Decomposition..

 

 

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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