Prove that for any initial state vector
as long as you begin with legitamite proportions (so that r0+p0+w0=1), after a long run you get the same result as
Sk= b1(Lambda1)^k [X1] + b2(Lambda2)^k[X2]+...+bn(Lambdan)^k[Xn]
The Attempt at a Solution
Ive tried to go about this by showing this works by choosing r0+p0+w0 to =1
and I've showed that if I do not begin with legitimate proportions it will fail
Would anyone be able to help to show this maybe using an actual equation like in a linear combination?
Id really appreciate your help:)