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-2 1 3 2 0 8 The matrix A = -4 1 12 2 0 –10 -4 2 7 can be written as A = LU, where L is a Lower Triangular Matrix and U is an Upper Triangular Matrix. Find L and U.

-2 1 3 2 0 8 The matrix A = -4 1 12 2 0 –10 -4 2 7 can be written as A = LU, where L is a Lower Triangular Matrix and U is an Upper Triangular Matrix. Find L and U.

Advanced Engineering Mathematics
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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The matrix A = (see image)

can be written as A = LU, where L is a Lower Triangular Matrix and U is an Upper Triangular Matrix.  Find L and U.

The matrix \( A \) is given by: \[ A = \begin{pmatrix} -2 & 1 & 3 \\ 2 & 0 & 8 \\ -4 & 1 & 12 \\ 2 & 0 & -10 \\ -4 & 2 & 7 \\ \end{pmatrix} \] This matrix can be written as \( A = LU \), where \( L \) is a Lower Triangular Matrix and \( U \) is an Upper Triangular Matrix. Find \( L \) and \( U \).
Transcribed Image Text:The matrix \( A \) is given by: \[ A = \begin{pmatrix} -2 & 1 & 3 \\ 2 & 0 & 8 \\ -4 & 1 & 12 \\ 2 & 0 & -10 \\ -4 & 2 & 7 \\ \end{pmatrix} \] This matrix can be written as \( A = LU \), where \( L \) is a Lower Triangular Matrix and \( U \) is an Upper Triangular Matrix. Find \( L \) and \( U \).
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