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find A and use it to compute the minimal length least squares solution to Ax b

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole ISBN: 9780538735452 298

Solution for problem 7.4.46 Chapter 7

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 7.4.46

find A and use it to compute the minimal length least squares solution to Ax b.

Step-by-Step Solution:
Step 1 of 3

S343 Section 3.6 Notes- Variation of Parameters 10-11-16  Variation of parameters- general method, can be applied in principle to any equation; no detailed assumptions about form of solution required ′′ ′  Consider + + = () where ,, continuous o Assume general homogeneous solution = + 1 1 ) 2 2( ) o Replace constants ,1 w2th functions 1 re2pectively; determine functions such that = 1 1 (2) sat2sfies original nonhomogeneous ODE ′ ′( ) ( ) ( ) ( ) ′( ) ( ) ( ) ( ) o Find = 1 +1 1 1 + 2 2 2 2 o Let 1 1+ 2 = 0,2so that = + 1 1 ) 2( ) (2) o Find = + ( ) ′′( + + ( ) ′() 1 1 1 1 2 2 2 2 o Substitute , ′, ′′ into ODE: ′( ) ( ) ( ) ′′( ) ′( ) ( ) ( ) ′( ) ( ) ( ) ( ) ( ) ( ) (1 1+ 1 1 + 2 2 2 2 ) + ( 1 +1 2 2 ) +

Step 2 of 3

Chapter 7, Problem 7.4.46 is Solved
Step 3 of 3

Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)
Edition: 3
Author: David Poole
ISBN: 9780538735452

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find A and use it to compute the minimal length least squares solution to Ax b