/*! 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} Q16E Consider the matrix 聽A=|abbc| w... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q16E (page 336)

Consider the matrix A=|abbc| where a, b, and c are nonzero constants. For which values of a, b, and c does A have two distinct eigenvalues?

Short Answer

Expert verified

Values of a, b, and c for which A have two distinct eigenvaluesa鈮�c,b鈮�0

Step by step solution

01

Eigenvalues

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled.

02

Step 2: Finding values of a, b, and c for which A have two distinct eigenvalues: 

We can clearly see that,

detA-位l=0deta-位bbc-位=0a-位c-位-b2=0位2-a+cc-位-b2=0位1,2=a+c卤a2+2ac+c2-4ac+b22=a+c卤a-c2+b22

Hence, a鈮�c,b鈮�0.

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

Is v鈬赌an eigenvector ofA+2In? If so, what is the eigenvalue?

Arguing geometrically, find all eigen vectors and eigen values of the linear transformations. In each case, find an eigen basis if you can, and thus determine whether the given transformation is diagonalizable.

The linear transformation withT(v鈫�)=v鈫�, and T(w鈫�)=v鈫�+w鈫�for the vectorsv鈫�andw鈫�inR2 sketched below.

find an eigenbasis for the given matrice and diagonalize:

A=[111111111]

For a given eigenvalue, find a basis of the associated eigenspace. Use the geometric multiplicities of the eigenvalues to determine whether a matrix is diagonalizable. For each of the matrices A in Exercises 1 through 20, find all (real) eigenvalues. Then find a basis of each eigenspace, and diagonalize A, if you can. Do not use technology

6.(2345)

For a given eigenvalue, find a basis of the associated eigenspace. Use the geometric multiplicities of the eigenvalues to determine whether a matrix is diagonalizable. For each of the matrices A in Exercises 1 through 20, find all (real) eigenvalues. Then find a basis of each eigenspace, and diagonalize A, if you can. Do not use technology

14.(100-500001)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.