Solve the system Ax = b using the given LU factorization of AA=\begin{bmatrix}-2 & 1 \\2 & 5 \end{bmatrix}=\begin{bmatrix}1 & 0 \\-1 & 1 \end{bmatrix}\begin{bmatrix}-2 & 1 \\0 & 6 \end{bmatrix}, b=\begin{bmatrix}5 \\1 \end{bmatrix}

Albarellak

Albarellak

Answered question

2021-05-04

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

Answer & Explanation

sweererlirumeX

sweererlirumeX

Skilled2021-05-05Added 91 answers

Step 1
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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