Find the LU factorization of 3 A = -9 13 3 -5 That is, write A = LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix. A
Find the LU factorization of 3 A = -9 13 3 -5 That is, write A = LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix. A
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Find the LU factorization of
-3
3
A
-9
13
%3D
-5
|
That is, write A = LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix.
A =
Expert Solution

Step 1
The following steps are used to obtain the LU factorization of the given matrix A.
- Apply the Gaussian elimination method, to convert the given matrix into an upper triangular matrix U.
- Write ones on the main diagonal and the multipliers that are used in the Gaussian elimination as the remaining terms of the lower triangular matrix L.
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