Recent content by cientifiquito

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    Powers of Markov transition matrices

    Homework Statement Prove the following theorem by induction: Let P be the transition matrix of a Markov chain. The ijth entry p(n)ij of the matrix Pn gives the probability that the Markov chain, starting in state si, will be in state sj after n steps. Homework Equations p(2)ij =...
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    Permutation and counting problem

    I see now, thanks henry_m
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    Permutation and counting problem

    Homework Statement Let r be a positive integer. For any number x, let (x)r = x(x-1)(x-2)...(x-r+1) Show that (-1/2)r = (-1)rr!2-2r(2r take r) Homework Equations by "2r take r" I mean what is usually denoted by (n / r) (written like a fraction but without the bar) and is calculated...
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    Dimension of vector space (proof)

    murmillo, That's exactly the leap I wasn't making--you just substitute T1 for v1 Thanks so much
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    Dimension of vector space (proof)

    Hi, I'm having trouble understanding a proof of the following theorem which allows it to be shown that all bases for a vector space have the same number of vectors, and that number is the dimension of the vector space (as you probably already know): Homework Statement Theorem: If S =...
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    Deriving equation for force from pressure that varies with water level

    Yes, thanks hage567.
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    Deriving equation for force from pressure that varies with water level

    Homework Statement Water is filled to a height H behind a dam of width w. Determine the resultant force exerted by the water on the dam. Homework Equations P=pgh = pg(H-y) (where p is density, greek rho) dF = PdA = pg(H-y)wdy (where dA is a narrow horizontal strip of the dam with...