Homework Help is Here – Start Your Trial Now!
Math
Algebra
Determine whether A -3 a is defective or not.

Determine whether A -3 a is defective or not.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
Determine whether A -3 a is defective or not.
Transcribed Image Text:Determine whether A -3 a is defective or not.
Expert Solution
Step 1

Given:

A=-11-1-3

To Determine:

A is defective or not.

Defective matrix:

A defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors.

 

Step 2

Here,

A=-11-1-3

First, the find eigenvalues and eigenvectors 

Start from forming a new matrix by subtracting λ from the diagonal entries of the given matrix:

A=-λ-11-1-λ-3

Find the determinant of the obtained matrix:

-λ-11-1-λ-3=λ2+4λ+4

λ2+4λ+4=(λ+2)2

⇒(λ+2)2=0

Thus, the root are λ1=-2 and λ2=-2

These are the eigen values.

steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS