Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. the following are the jordan canonical form of lin

The following are the Jordan Canonical Form of linear transformations. Find the characteristic polynomial, minimal...

Free

70.2K

Verified Solution

Question

Advance Math

The following are the Jordan Canonical Form of linear transformations. Find the characteristic polynomial, minimal polynomials, the algebraic multiplicity, geometric multiplicity and the index of each of the eigenvalues of L.

A=( egin{pmatrix}2&0&0&0\ 0&2&0&0\ 0&0&1&0\ 0&0&0&3end{pmatrix} )

Answer & Explanation Solved by verified expert
4.2 Ratings (607 Votes)

Solution

A=( egin{pmatrix}2&0&0&0\ 0&2&0&0\ 0&0&1&0\ 0&0&0&3end{pmatrix} )

The characteristics polynomial. ( implies P(lambda)=|A-lambda I|=igg(2-lambdaigg)^2igg(1-lambdaigg)igg(3-lambdaigg)hspace{2mm} )

The algebraic multiplicity

( implies am(2)=2,am(1)=1,am(3)=1 hspace{2mm} )

The geometric multiplicity

( implies gm(2)=2,gm(1)=1,gm(3)=1hspace{2mm} )

The ( indeximplies Index(2)=1,Index(1)=1,Index(3)=1 hspace{2mm} )

The minimal polynomial

( implies m(lambda)=igg(lambda-1igg)igg(lambda-1igg)igg(lambda-3igg)hspace{2mm} )

Answer :

Therefore .

( implies P(lambda)=|A-lambda I|=igg(2-lambdaigg)^2igg(1-lambdaigg)igg(3-lambdaigg)hspace{2mm} )

( implies am(2)=2,am(1)=1,am(3)=1 hspace{2mm} )

( implies gm(2)=2,gm(1)=1,gm(3)=1hspace{2mm} )

( implies Index(2)=1,Index(1)=1,Index(3)=1 hspace{2mm} )
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Basic Math
1.2K views

A company is creating a new fertilizer additive for lawn seed, which will be a mixture...

Finance
1.2K views

Compare the financial reports from Disney, Hilton Worldwide, Starwood, Intercontinental, Marriott International, and Marriott Vacations. Disney Company: Report Date 09/29/2018 09/30/2017 10/01/2016 10/03/2015 09/27/2014 Total...

Psychology
1.2K views

Please give an overview as to how memories are formed and stored in your brain. For...

Biology
1.2K views

Over evolutionary time, flowering plants have evolved colors, odors, and nectar that attract pollinating insects...

Biology
1.2K views

Discussion Board Topic: This are the questions you need to answer: In mammals, males often...

Basic Math
1.2K views

Mariah buys a bag of cookies that contains 4 chocolate chip cookies, 6 peanut butter...

Algebra
1.2K views

Let A B and C lie on the same line I in each of the...

Accounting
1.2K views

Which of the following costs are NOT variable? 1 and 2 1 and 4 only...

Accounting
1.2K views

Whistle-blowers: Have no role in an FFCA case once it starts. Usually get...

Accounting
1.2K views

list and describe four non-income-based taxes. be sure to categorize each tax as either progressive...

Accounting
1.2K views

An investor has asked for your help with the following time value of money applications....

Accounting
1.2K views

Help me correct the two incorrect answers outlined in red for this intermediate accounting 2...