Transition Matrix/Markov Process

Question

Let P be a 2x2 transition matrix for a markov process

row 1 [.4 .7]

row 2 [.6 .3]

If the current distribution is given by a 2x1 matrix,

row 1[.8]

row 2[.2]

what will the distribution be after one time interval?

Answer 1

We calculate Px

.4 * .8 + .7 * .2

.6 * .8 + .3 * .2

.46

.54