[[.8, 0, 1/3], [.2, .5, 0], [0, .5, 2/3]]^23 * [[100], [0], [0]]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.