/*! 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} Q35E Give an example of a 4脳4聽matri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q35E (page 383)

Give an example of a 4脳4matrix A without real eigenvalues.

Short Answer

Expert verified

Matrix a without real eigenvalues.

For a characteristic polynomial will be:

(a-位)(b-位)(c-位)(d-位)=0A=i0000i0000-i0000-i

It is not given A is real matrix. hence, we can do the above.

Step by step solution

01

definition of polynomial

A polynomial is a mathematical expression made up of in determinates and coefficients that only involves the operations of addition, subtraction.

Example of a 4脳4matrix A without real eigenvalues:

Let us assume a to be diagonal with elements a, b, c, d.

Now eigen values are the root of characteristic polynomial.

For a characteristic polynomial will be:

(a-位)(b-位)(c-位)(d-位)=0

02

definition Required example

The required example is the:

Roots of are a,b,c,d

As 位is non-real we can take a,b,c,d as any complex nos.

one example is a = i b = i c = -l d = -i

Required example:A=i0000i0000-i0000-i

Hence, it is not given a is real matrix hence we can do the above.

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

Consider the matrix A=|abba|where aand bare arbitrary constants. Find all eigenvalues of A.

For an arbitrary positive integer n, give a 2n脳2n matrix A without real eigenvalues.

find an eigenbasis for the given matrice and diagonalize:

A=17[6-2-3-23-6-3-6-2]

Representing the reflection about a plane E.

For m鈮�n, find the dimension of the space of alln脳nmatricesfor which all the vectorse鈬赌1,....,e鈬赌mare eigenvectors.

find an eigenbasis for the given matrice and diagonalize:

A=[111111111]
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Pure 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.