This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: row of A with the j th column of B ; that is, to a i 1 a n 1 b 1 j . . . b nj = a i 1 b 1 j + + a n 1 b nj . 1 Note that, since all the numbers on the righthand side are nonnegative, the term on the righthand side is nonnegative. The sum of the entries in the i th row of AB is equal to n X j =1 ( a i 1 b 1 j + + a n 1 b nj ) = a i 1 n X j =1 b 1 j + + a n 1 n X j =1 b nj . Since B is a right stochastic matrix, we have n X j =1 b 1 j = = n X j =1 b nj = 1 . Thus the sum of the entries in the i th row of AB is equal to a i 1 + + a n 1 ; and since A is a right stochastic matrix, this is equal to 1. This the sum of the entries in each row of AB is equal to 1. 2...
View
Full
Document
This note was uploaded on 03/19/2009 for the course M m136 taught by Professor Fokshuen during the Spring '09 term at Waterloo.
 Spring '09
 FokShuen
 Algebra

Click to edit the document details