[2 1 -1 5) Suppose A = |1 3 1 -2 0 2 1 -5 1. a) Find elementary matrices E1,..., Em which are lower triangular and have ones on the diag- onal, such that EM……E, A is an upper trianular matrix U. b) Using your solution from a), find a lower triangular matrix L with ones on the diagonal such that A = LU. *c) What is th smallest value of M for which this is possible? Can you prove that you have the correct answer?
[2 1 -1 5) Suppose A = |1 3 1 -2 0 2 1 -5 1. a) Find elementary matrices E1,..., Em which are lower triangular and have ones on the diag- onal, such that EM……E, A is an upper trianular matrix U. b) Using your solution from a), find a lower triangular matrix L with ones on the diagonal such that A = LU. *c) What is th smallest value of M for which this is possible? Can you prove that you have the correct answer?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.5: Applications
Problem 30EQ
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