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- bob bundy
- 2012-11-21 02:44:26
Good question. I abandoned that idea and went for a aij type proof instead. It's just in my head so who knows how it will look when it goes down in type.
Bob
- anonimnystefy
- 2012-11-21 01:02:49
Hi Bob
How would you do an iinductive proof here?
- bob bundy
- 2012-11-21 00:59:20
I think I can put together a proof for n x n if you wish.
Bob
- bob bundy
- 2012-11-20 21:17:32
Just gone a step further, which may then lead to an inductive proof.
If A and B are 2 x 2 matrices having the property, the AB has the property.
Bob
- bob bundy
- 2012-11-20 21:09:00
hi princess snowwhite
Just proved it is true for all 2 x 2 matrices (algebraically). Don't think I can generalise that method of proof though. 
Bob
- bobbym
- 2012-11-20 21:03:55
Then I would say the answer is yes but I do not remember how to prove that.
- princess snowwhite
- 2012-11-20 20:58:48
Yes It Does Mean That Each Roq Sums To 1
- bobbym
- 2012-11-20 20:57:13
Hi princess snowwhite;
I am not sure about the term row sum. If you mean that each row sums to 1 then the matrix is called stochastic and is used in Markov processes. Every integer power of that matrix will also be stochastic meaning the rows sum to 1. So, I would say yes.
- princess snowwhite
- 2012-11-20 20:00:09
let P be any n*n square matrix whose row sum equals 1 then for any postive m the row sum of the matrix P^m equals 1 ,state true or false