Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. 1. for each matrix a below compute the characteris

1. For each matrix A below compute the characteristic polynomial χA(t) and do a direct matrix...

50.1K

Verified Solution

Question

Advance Math

1. For each matrix A below compute the characteristic polynomialχA(t) and do a direct matrix computation to verify that χA(A) =0.

(4 3

-1 1)    (2 1 -1 0 3 0 0 -1 2) (3*3 matrix)

2.  For each 3*3 matrix and each eigenvalue belowconstruct a basis for the eigenspace Eλ.

A= (9 42 -30 -4 -25 20 -4 -28 23),λ = 1,3
A= (2 -27 18 0 -7 6 0 -9 8) , λ = −1,2

3. Construct a 2×2 matrix with eigenvectors(4 3) and (−3 −2)with eigen-values 2 and −3, respectively.

4. Let A be the 6*6 diagonal matrix below. For each eigenvalue,compute the multiplicity of λ as a root of the characteristicpolynomial and compare it to the dimension of the eigenspaceEλ.

(x 0 0 0 0 0 0 x 0 0 0 0 0 0 y 0 0 0 0 0 0 x 0 0 0 0 0 0 z 0 0 00 0 0 x)

5.   Let A be an 3*3 upper triangular matrix with alldiagonal elements equal, such as (3 4 -2 0 3 12 0 0 3)

Prove that A is diagonalizable if and only if A is a scalartimes the identity matrix.

Answer & Explanation Solved by verified expert
3.6 Ratings (419 Votes)
    See Answer
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

Finance
1.2K views

Choco Inc. buys chocolate from Switzerland and resells it in the U.S. It just purchased chocolate...

Advance Math
1.2K views

**MATLAB 8)The structure for students' quiz data for a class is organized as below ID number Quiz 44 7 33 5.5 37 8 write a script...

Advance Math
1.2K views

Among the tools (e.g., graphics tools, knowledge-based tools, etc.), determine the type of tool that you...

Physics
1.2K views

1 The dimensionally correct expression for resistance R among the following is P electric power...

Algebra
1.2K views

Multiply 81 x X Select the correct choice below and fill in any answer boxes...

Accounting
1.2K views

The standard direct labor cost for producing one unit of product is 5.7 direct labor...

Accounting
1.2K views

Q. When is an activity-based costing system better than a traditional allocation system

Accounting
1.2K views

On September 7, the billing date, Verna had a balance due of $565.85 on her...

Accounting
1.2K views

PLEASE ANSWER ALL! THANK YOU! The law firm of Prawitt and Bradford accumulates costs...

Finance
1.2K views

QUESTION 13 If both Pepsi and coke have expected returns of 5%, and Pepsi has...

Accounting
1.2K views

Question 10 During 2017, Bramble Furniture Company purchases a carload of wicker chairs. The manufacturer...

Accounting
1.2K views

Screeching Meadows sells Halloween Costumes for small children. Evaluate the inventory using the lower of...