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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...
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