Determine whether the stochastic matrix P is regular. Then find the steady state matrix X of the Markov chain with matrix of transition probabilities P. P= 0.22 0.20 0.65
0.62 0.60 0.15
0.16 0.20 0.20

Step-by-step explanation:

Given that:

For a steady-state of a given matrix

As a result P = and a+b+c must be equal to 1

So, if P =

Then;

Equating both equation (1) and (3)

(0.22a+ 0.2b + 0.65c) - (0.16a + 0.2b + 0.2c) = a - c

0.06a + 0.45c = a - c

collect like terms

0.06a - a = -c - 0.45c

-0.94 a = -1.45 c

0.94 a = 1.45 c

Using equation (2)

0.62a + 0.60b + 0.15c = b

where;

c = 94/145 a

From a + b + c = 1

∴

∴

The steady matrix of is:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

15.36 per mile

but forgot to round

i am pretty sure