Solve the system Ax = b using the given LU

obrozenecy6

obrozenecy6

Answered question

2021-12-07

Solve the system Ax = b using the given LU factorization of A
A=[2125]=[1011][2106],b=[51]

Answer & Explanation

Jenny Bolton

Jenny Bolton

Beginner2021-12-08Added 32 answers

Step 1
Given:
A=[2125]=[1011][2106],b=[51]
Step 2
A=[1011][2106]=LU
Let Y=UX; (y1y2)=[2106][x1x2]
Let LY=b; [1011](y1y2)=[51]
Solve:
y1=5
y1+y2=15+y2=1y2=6
Now solve Y=UX; y1=2x1+x2;y2=0x1+6x2
Substituting the value of y1 and y2
6=6x2x2=1
5=2x1+12x1=4x1=2
Answer:
(x1,x2)=(2,1)

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