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10. LU decomposition using Crout's method of matrix example ( Enter your problem )
  1. Example [8-62-67-42-43]
  2. Example [324202423]
  3. Example [111-1-3-3244]
  4. Example [23410]
Other related methods
  1. Transforming matrix to Row Echelon Form
  2. Transforming matrix to Reduced Row Echelon Form
  3. Rank of matrix
  4. Characteristic polynomial of matrix
  5. Eigenvalues
  6. Eigenvectors (Eigenspace)
  7. Triangular Matrix
  8. LU decomposition using Gauss Elimination method of matrix
  9. LU decomposition using Doolittle's method of matrix
  10. LU decomposition using Crout's method of matrix
  11. Diagonal Matrix
  12. Cholesky Decomposition
  13. QR Decomposition (Gram Schmidt Method)
  14. QR Decomposition (Householder Method)
  15. LQ Decomposition
  16. Pivots
  17. Singular Value Decomposition (SVD)
  18. Moore-Penrose Pseudoinverse
  19. Power Method for dominant eigenvalue
  20. determinants using Sarrus Rule
  21. determinants using properties of determinants
  22. Row Space
  23. Column Space
  24. Null Space

1. Example [8-62-67-42-43]
(Previous example)
3. Example [111-1-3-3244]
(Next example)

2. Example [324202423]





Find LU decomposition using Crout's method of Matrix ...
[324202423]


Solution:
Crout's method for LU decomposition
Let A=LU

324
202
423
 = 
l1100
l21l220
l31l32l33
 × 
1u12u13
01u23
001


324
202
423
 = 
l11l11u12l11u13
l21l21u12+l22l21u13+l22u23
l31l31u12+l32l31u13+l32u23+l33


This implies
l11=3

l11u12=23×u12=2u12=23

l11u13=43×u13=4u13=43



l21=2

l21u12+l22=02×23+l22=0l22=-43

l21u13+l22u23=22×43+(-43)×u23=2u23=12



l31=4

l31u12+l32=24×23+l32=2l32=-23

l31u13+l32u23+l33=34×43+(-23)×12+l33=3l33=-2



A=L×U=LU

324
202
423
 = 
300
2-430
4-23-2
 × 
12343
0112
001
 = 
324
202
423



This material is intended as a summary. Use your textbook for detail explanation.
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1. Example [8-62-67-42-43]
(Previous example)
3. Example [111-1-3-3244]
(Next example)





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