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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

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.  sad

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

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