Find an LU factorization of the matrix A (with L unit lower triangular). A=[(5,4),(-4,-3)] L-? U-?

FizeauV 2021-02-10 Answered
Find an LU factorization of the matrix A (with L unit lower triangular).
A=[5443]
L-?
U-?
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Expert Answer

StrycharzT
Answered 2021-02-11 Author has 102 answers
Step 1
Given that,
A=[5443]
A=LU
A=LU=[10L211][U11U120U22]=[U11U12L21U11L21U12+U22]
[5443]=[U11U12L21U11L21U12+U22]
Step 2
By comparing the matrices,
U11=5,U12=4
L21U11=4L21(5)=4L21=45
L21U12+U22=345(4)+U22=3U22=3+165U22=15
We have,
L=[10L211],U=[U11U120U22]
Plug the know values in matrices, get
L=[10451],U=[54015]
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