Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Form the converse, inverse, and contrapositive of the statement: "If an n x n matrix A has n distinct real eigenvalues, then A is diagonalizable." Which of them are true?

Form the converse, inverse, and contrapositive of the statement: "If an n x n matrix A has n distinct real eigenvalues, then A is diagonalizable." Which of them are true?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Form the converse, inverse, and contrapositive of the statement: "If an n x n matrix A has n distinct real eigenvalues, then A is diagonalizable." Which of them are true?
Transcribed Image Text:Form the converse, inverse, and contrapositive of the statement: "If an n x n matrix A has n distinct real eigenvalues, then A is diagonalizable." Which of them are true?
Expert Solution
Step 1

Given statement is

"If an n x n matrix A has n distinct real eigenvalues, then A is diagonalizable."

p=n x n matrix has n distinct real eigenvalues

q= A is diagonalizable

Given statement is    p→q

Converse Statement is q→p

"If A is diagonalizable, then an n x n matrix A has n distinct real eigenvalues"

Inverse statement is ~p→~q

"If an n x n matrix A has not n distinct real eigenvalues, then A is not diagonalizable."

 Contrapositive statement is ~q→~p

"If A is not diagonalizable, then an n x n matrix A has not n distinct real eigenvalues"

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Matrix Eigenvalues and Eigenvectors
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS