The aim of this question is to assess your understanding of elementary matrices and the LU decomposition of a matrix. (a) Determine, by hand, the elementary matrices Eįj that represent the elementary row operations used in applying Gaussian elimination to the matrix A = -1 3 -31 3 4 5 2 -1 8 - to transform A to upper triangular form. (b) Deduce the LU decomposition of A, and use it to solve the following system of linear equations. -x₁ + 3x₂ − 3x3 = = 14, 3x14x2 + 5x3 = -23, 2x1 x₂ + 8x3 = -15.
The aim of this question is to assess your understanding of elementary matrices and the LU decomposition of a matrix. (a) Determine, by hand, the elementary matrices Eįj that represent the elementary row operations used in applying Gaussian elimination to the matrix A = -1 3 -31 3 4 5 2 -1 8 - to transform A to upper triangular form. (b) Deduce the LU decomposition of A, and use it to solve the following system of linear equations. -x₁ + 3x₂ − 3x3 = = 14, 3x14x2 + 5x3 = -23, 2x1 x₂ + 8x3 = -15.
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:The aim of this question is to assess your understanding of elementary
matrices and the LU decomposition of a matrix.
(a) Determine, by hand, the elementary matrices Eįj that represent the
elementary row operations used in applying Gaussian elimination to the
matrix
A
=
-1 3
-31
3
4
5
2 -1 8
-
to transform A to upper triangular form.
(b) Deduce the LU decomposition of A, and use it to solve the following
system of linear equations.
-x₁ + 3x₂ − 3x3 =
=
14,
3x14x2 + 5x3 = -23,
2x1 x₂ + 8x3 = -15.
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