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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 =
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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