Problem 1: Consider the systems of equations below. For each system, write it as Ar = b, and then try to perform the LU factorization on A (note this means you should not include the "b" portion of the augmented matrix!): (a) The system (b) The system 2x + y + z = 180 x + 3y + 2z = 300 2x + y + 2z = 140 3x1 3x1 + 3x2 7x2 + 9x2 + 6x3 8x3 12x3 + 6x4 + 4x5 5x4 + 8x5 =-5 = 9 9x4 + 6x5 = 15 What goes wrong with the LU factorization if we use the row swap elementary operation? Hint: Think about what the corresponding E; would be in contrast with the importance of the letter L.
Problem 1: Consider the systems of equations below. For each system, write it as Ar = b, and then try to perform the LU factorization on A (note this means you should not include the "b" portion of the augmented matrix!): (a) The system (b) The system 2x + y + z = 180 x + 3y + 2z = 300 2x + y + 2z = 140 3x1 3x1 + 3x2 7x2 + 9x2 + 6x3 8x3 12x3 + 6x4 + 4x5 5x4 + 8x5 =-5 = 9 9x4 + 6x5 = 15 What goes wrong with the LU factorization if we use the row swap elementary operation? Hint: Think about what the corresponding E; would be in contrast with the importance of the letter L.
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:Problem 1: Consider the systems of equations below. For each system, write it as Ax = b, and
then try to perform the LU factorization on A (note this means you should not include the “b” portion of the augmented
matrix!):
(a) The system
(b) The system
2x + y + z = 180
x + 3y + 2z = 300
2x + y + 2z = 140
3x1
3x1
6x3
7x2 +
813
9x2 + 12x3
+ 3x2
+ 6x4 + 4x5
=-5
= 9
5x4 + 8x5
9x4 + 6x5 = 15
What goes wrong with the LU factorization if we use the row swap elementary operation? Hint: Think
about what the corresponding E; would be in contrast with the importance of the letter L.
Expert Solution
Step 1
In this solution we will discuss the decomposition of the corresponding coefficient matrices of the given system of equations.
decomposition of a matrix is a factorization of a matrix in terms of product of lower and upper triangular matrices.
The given system of equations are:
(a)
(b)
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