/*! 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} Q32E If A is any transition matrix an... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q32E (page 108)

If A is any transition matrix and B is any positive transition matrix, then AB must be a positive transition matrix.

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Explaining

Let A be a transition matrix and B a positive transition matrix. By definition, every column of A is a distribution vector and sums to one. Thus, A cannot contain any all-zero columns. However, A could contain an all-zero row. For example, the matrix0001214012321 is a transition matrix.

02

Result

The (i,j)th entry of the matrix AB is the dot product of the ith row of A and the column of B. Since the row of A could be all zero, the dot product could be zero. Therefore, the matrix AB is not necessarily a positive transition matrix and the answer 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

If matrices A and B commute, then the formula A2B = BA2 must hold.

IfAB=lnfor twon脳nmatrices Aand B, then Amust be the inverse of B.

If A is a 3脳4matrix and B is a4脳5, then AB will be a5脳3matrix.

Give a geometric interpretation of the linear transformations defined by the matrices in Exercises 16through 23 . Show the effect of these transformations on the letter L considered in Example 5 . In each case, decide whether the transformation is invertible. Find the inverse if it exists, and interpret it geometrically. See Exercise 13.

21. [01-10]

TRUE OR FALSE?

For every regular transition matrix Athere exists a transition matrix Bsuch that AB=B.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.