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1. Given the real symmetric matrix A: 1 -1 A 8 -4 -1 -4 7 (a) Construct a unit lower triangular matrix L that will undo those row ops, so that A = LU. (b) Show that U can be written as D LT, wherer D is a diagonal matrix with the same diagonal elements as U. (c) Find L1 = L D'/2, and show that A = L1 L7.

1. Given the real symmetric matrix A: 1 -1 A 8 -4 -1 -4 7 (a) Construct a unit lower triangular matrix L that will undo those row ops, so that A = LU. (b) Show that U can be written as D LT, wherer D is a diagonal matrix with the same diagonal elements as U. (c) Find L1 = L D'/2, and show that A = L1 L7.

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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1. Given the real symmetric matrix A: -1 A 8 -4 -1 -4 7 (a) Construct a unit lower triangular matrix L that will undo those row ops, so that A = LU. (b) Show that U can be written as D LT, wherer D is a diagonal matrix with the same diagonal elements as U. (c) Find L1 = L D'/2, and show that A = L1 L7.
Transcribed Image Text:1. Given the real symmetric matrix A: -1 A 8 -4 -1 -4 7 (a) Construct a unit lower triangular matrix L that will undo those row ops, so that A = LU. (b) Show that U can be written as D LT, wherer D is a diagonal matrix with the same diagonal elements as U. (c) Find L1 = L D'/2, and show that A = L1 L7.
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