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..
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
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe92e190-21eb-4bbd-ab9b-abe2398bf339%2F117804f2-4ef4-4e89-acf3-03f2f29a1843%2Fz6eqc1b_processed.jpeg&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe92e190-21eb-4bbd-ab9b-abe2398bf339%2F117804f2-4ef4-4e89-acf3-03f2f29a1843%2Frlzjy1r_processed.jpeg&w=3840&q=75)
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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