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A matrix .. is nilpotent if. _P _ for some positive integer p. The least such integer p

Linear Algebra with Applications | 8th Edition | ISBN: 9781449679545 | Authors: Gareth Williams ISBN: 9781449679545 435

Solution for problem 18 Chapter 2

Linear Algebra with Applications | 8th Edition

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Linear Algebra with Applications | 8th Edition | ISBN: 9781449679545 | Authors: Gareth Williams

Linear Algebra with Applications | 8th Edition

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Problem 18

A matrix .. is nilpotent if. _P _ for some positive integer p. The least such integer p is called the degree of nilpotency. Prove that if A is nilpotent, then A1 is also nilpotent with the same degree of nil potency.

Step-by-Step Solution:
Step 1 of 3

M303 Section 1.8 Notes- Introduction to Linear Maps/Transformations 9-19-16 n  If A is m×n matrix, them for any vector xϵR , mulmiplication by A produces new vector A x ϵR ; if we regard vectors in R as inputs on which A acts by multiplication to give output iR m , and we arrive at notion of a function  Function/map n m - rule which assigns unique output m to each n T:R → R T(x)ϵR input xϵR n m R R goes from domain to ta

Step 2 of 3

Chapter 2, Problem 18 is Solved
Step 3 of 3

Textbook: Linear Algebra with Applications
Edition: 8
Author: Gareth Williams
ISBN: 9781449679545

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A matrix .. is nilpotent if. _P _ for some positive integer p. The least such integer p