## Solution for problem 22 Chapter 2.7

# Solved: Questions 22-24 are aboutthe factorizations PA = L U and A = LIP 1 U 1-

Introduction to Linear Algebra | 4th Edition

Questions 22-24 are aboutthe factorizations PA = L U and A = LIP 1 U 1-

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M303 Section 5.3 Notes- Diagonalization 12-7-16 Recall diagonal matrix- only (possible) nonzero entries are on diagonal o Ex. Simple to compute powers 5 0 2 5 0 5 0 52 0 [0 3] = [0 3 0 3 ]= [ 2] 3 2 02 3 3 [5 0] = [5 0 ] [5 0]= [5 0 ][5 0]= [5 0 ] 0 3 0 3 0 3 0 3 2 0 3 0 33 5 0 5 0 [0 3] = [0 3] o Commute in multiplication Not all matrices can be diagonal, but class of diagonalizable matrices exists that has many of same properties of diagonal matrices o × matrix diagonali

###### Chapter 2.7, Problem 22 is Solved

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Solved: Questions 22-24 are aboutthe factorizations PA = L U and A = LIP 1 U 1-