/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q25E TRUE OR FALSEAll lower triangula... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q25E (page 383)

TRUE OR FALSE

All lower triangular matrices are diagonalizable (over C ).

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Define lower triangular matrix

A lower triangular matrix is that square matrix whose all the entries above the main diagonal are 0.

02

Explanation

For example, consider the matrix

A=0020

Which is a lower-triangular matrix, however, its only eigenvalue is位=0, with algebraic multiplicity 2 and geometric multiplicity 1, so A is not diagonalizable.

Hence, the given statement is false.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformations in Exercises 15 through 22. In each case, find an eigenbasis if you can, and thus determine whether the given transformation is diagonalizable.

Rotation through an angle of 180掳inR2.

If a vector v鈬赌is an eigenvector of both Aand B, isv鈬赌necessarily an eigenvector of A+B?

Find all2脳2matrices for whiche鈬赌1is an eigenvector.

Suppose v鈨�Supposeis an eigenvector of the n脳nmatrix A, with eigenvalue 4 . Explain why v鈨�is an eigenvector of A2+2A+3In.What is the associated eigenvalue?

Is v鈬赌an eigenvector ofA3 ? If so, what is the eigenvalue?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.