Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Linear Algebra With Applications
Found in: Page 108
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.


Short Answer

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

The statement is false.

See the step by step solution

Step by Step Solution

Step 1: 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 matrix 0001214012321 is a transition matrix.

Step 2: 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.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.