Find an LU factorization of the matrix A (with L unit lower triangular). A=[(-4,0,4),(12,2,-9),(12,8,9)] L-? U-?

tabita57i 2020-12-12 Answered
Find an LU factorization of the matrix A (with L unit lower triangular).
A=[40412291289]
L-?
U-?
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Expert Answer

bahaistag
Answered 2020-12-13 Author has 101 answers
Step 1
The given matrix is A=[40412291289].
Using Gaussian Elimination method,
A=[4040231289]R2R2+3R1
=[4040230821]R3R3+3R1
=[404023009]R3R34R2
Step 2
Since, U=[404023009].
L is just up of the multipliers we used in Gaussian elimination with ls on the diagonal.
Since, L=[100310341].
Hence Lu decomposition for A is
A=[40412291289]=[100310341][404023009]=LU.
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