Compute the LU factorization of each of the following matrices. begin{bmatrix}1 & 1&1 3 & 5&6-2&2&7 end{bmatrix}

tinfoQ 2020-11-12 Answered
Compute the LU factorization of each of the following matrices.
[111356227]
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Expert Answer

l1koV
Answered 2020-11-13 Author has 100 answers
Step 1: to determine
Given:
A=(111356227) to determine:
LU decomposition of given matrix
Step 2: calculation
Calculation:
Let(111356227)=(l1100l21l220l31l32l33)(u11u12u130u22u2300u33)
Let lij=1f or i=j
So, (111356227)=(100l2110l31l321)(u11u12u130u22u2300u33)
Now multiplying two matrices on RHS , we get,
(111356227)=(u11u12u13l21u11l21u12+u22l21u13+u23l31u11l31u12+l32u22l31u13+l32u23+u33)
Step 3
Now , equating each entry , we get
u11=1
u12=1
u13=1
l21u11=3l211=3l21=3
l21u12+u22=53.1+u22=5u22=2
l21u13+u23=63.1+u23=6u23=3
l31u11=2l311=2l31=2
l31u12+l32u22=22.1+l322=2l32=2
l31u13+l32u23+u33=72.1+2.3+u33=7u33=3
So,
Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

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