Solve the system Ax = b using the given LU factorization

vazelinahS

vazelinahS

Answered question

2021-05-19

Solve the system Ax=b using the given LU factorization of A
A=[240314122]=[10032101201]×[240054002],b=[205]

Answer & Explanation

Nicole Conner

Nicole Conner

Skilled2021-05-20Added 97 answers

Step 1
Given matrices are,
A=[240314122]=[10032101201][240054002]=LU
b=[205]
Step 2
Solving for AX=(LU)x=b.
Consider y=Ux and solve for Ly=b.
Ly=b
[10032101201][y1y2y3]=[205]
y1=2,32y1+y2=0.12y1+y3=5
[y1y2y3]=[234]
Step 3
Similarly,
Ux=y
[240054002]=[x1x2x3]=[234]
2x14x2=2,5x2+4x3=3,2x3=4
[x1x2x3]=[312]

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