/*! 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} Q58E In Exercises 55 through 64, find... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q58E (page 86)

In Exercises 55 through 64, find all matricesX that satisfy the given matrix equation.

X2142=0000

Short Answer

Expert verified

The matrix X that will satisfy the equation will be-2cc-2dd , where are constants.

Step by step solution

01

Assuming the matrix

Since, the product of matrix gives 2脳2matrix then the order of matrix X should be 2脳2

Let the matrix beX=acbd .

Then the equation will become

acbd2142=0000

02

Solving the Matrix

To solve the given matrix equation, first multiply the left-hand side matrix.

2a+4ca+2c2b+4db+2d=0000

Now, equating the left-hand and right-hand matrix.

2a+4c=0a+2c=02b+4d=0b+2d=0

On solving the above equations, we will get

a=-2c,b=-2d,c=d,d=d

Hence, the matrix X that will satisfy the equation will be-2cc-2dd , where are constants.

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

A nonzero matrix of the form A=[a-bba] represents a rotation combined with ascaling. Use the formula derived in Exercise 2.1.13 to find the inverse of A .Interpret the linear transformation defined byA-1 geometrically. Explain.

The function T[xy]=[x-yy-x]is a linear transformation?

Question: Show that if A and B are nxn transition matrices, then AB will be a transition matrix as well. Hint: Use Exercise 67b.

Which of the functions f from R toR in Exercises 21 through 24 are invertible?22 f(x)=2x.

In this exercise we will verify part (b) of Theorem 2.3.11 in the special case when A is the transition matrix [0.40.30.60.7]andx炉is the distribution vector[10]. [We will not be using parts (a) and (c) of Theorem 2.3.11]. The general proof of Theorem 2.3.11 runs along similar lines, as we will see in Chapter 7.

  1. ComputeA[12]andA[1-1]. WriteA[1-1]as a scalar multiple of the vector[1-1].
  2. Write the distribution vectorx鈫�=[10]as a linear combination of the vectors[12]and[1-1]
  3. Use your answers in part (a) and (b) to writeAx鈫�as a linear combination of the vectors[12]and[1-1]. More generally, write Amx鈫�as a linear combination of vectors[12]and[1-1], for any positive integer m. See Exercise 81.
  4. In your equation in part (c), let got to infinity to find limm鈫�鈭�Amx鈫�. Verify that your answer is the equilibrium distribution for A.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Decision Maths

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.