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## Homework Statement

Prove that for any initial state vector

S0=

[r0

p0

w0]

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=

[1/4

1/2

1/4]

## Homework Equations

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:)