[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
icon
Related questions
Question
[2 1
-1
1.
5) Suppose A = |1 3 1
0 2 1
-2
-5
a) Find elementary matrices E1,..., Em which are lower triangular and have ones on the diag-
onal, such that Em ·…E1 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?
Transcribed Image Text:[2 1 -1 1. 5) Suppose A = |1 3 1 0 2 1 -2 -5 a) Find elementary matrices E1,..., Em which are lower triangular and have ones on the diag- onal, such that Em ·…E1 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?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,