Using the LU factorization, solve the following linear system 2х, + 4x3 + 10x4 = 18 -2x1 + 3 x2 - 6x3 + x4 = -11 4x1 + 3x2 – 7x3 + 5x4 = 30 + 15x3 + 12x4 = 9 6x1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Using the LU factorization, solve the following linear system
4x3 + 10x4 = 18
-2x1 + 3 x2 - 6x3 + x4 = -11
4x1 + 3x2 — 7хз + 5х4 3 30
+ 15х3 + 12хд 3D 9
Hint: Reduce the coefficient matrix to upper triangular matrix U using the multipliers and the
required row operation. No need to show the elimination matrices. Then use the multipliers to
2x1 +
|
6x1
find the lower triangular matrix L.
Transcribed Image Text:Using the LU factorization, solve the following linear system 4x3 + 10x4 = 18 -2x1 + 3 x2 - 6x3 + x4 = -11 4x1 + 3x2 — 7хз + 5х4 3 30 + 15х3 + 12хд 3D 9 Hint: Reduce the coefficient matrix to upper triangular matrix U using the multipliers and the required row operation. No need to show the elimination matrices. Then use the multipliers to 2x1 + | 6x1 find the lower triangular matrix L.
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