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Question

In the LU decomposition of the matrix [2249] if the diagonal elements of U are both 1, then the lower diagonal entry l22 of L is

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Solution

A=LU
[2249]=[l110l21l22][1u1201]
Comparing the correspondig elements on the both sides,
2=l11
(2=l_{11}.u_{12}\Rightarrow u_{12}=1\)
4=l21
9=l21.u12+l229=4×l+l22
l22=5

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