Let a linear sytem of equations Ax=b where A=begin{pmatrix}4 & 2&-2 2 & 2&-3-2&-3&14 end{pmatrix} , b=begin{pmatrix}10 , 5 , 4 end{pmatrix}^T in case we solve this equation system by using Dolittle LU factorization method , find Z and X matrices

Lewis Harvey 2021-03-12 Answered
Let a linear sytem of equations Ax=b where
A=(4222232314),b=(10,5,4)T
in case we solve this equation system by using Dolittle LU factorization method , find Z and X matrices
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Expert Answer

ottcomn
Answered 2021-03-13 Author has 97 answers

Step 1
By using Dolitte LU decomposition method ,
A=LU
[4222232314]=[100L2110L31L321][u11u12u130u22u2300u33]
[4222232314]=[u11u11u11u11L21L21u12+u22L21u13+u23L31u11u12L31+L32u22L31u13+L32u23+u33]
Step 2
By comparing the two matrices we will get,
u11=4
u12=2
u13=2
u11L21=2
4L21=2
L21=0.5
L21u12+u22=2
u22=2
L21u13+u23=3
u23=2
L31u11=2
L31=0.5
u12L31+L32u22=3
L32=0.5
L31u13+L32u23+u33=14
u33=9
Step 3
Therefore, the matrices L and U will be ,
L=[1000.5100.521]
U=[422012009] Let Lz=b where z=[z1z2z3]
Therefore, we will get ,
[1000.5100.521][z1z2z3]=[1054]
Step 4
From these we get,
z1=10
0.5z1+z2=5
z2=0
12z12z2+z3=4
z3=9
Thus t

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Jeffrey Jordon
Answered 2022-01-29 Author has 2047 answers

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