Approximate the stationary matrix S for the transition matrix P by computing powers of the transition matrix P. P = [0.31 0.69
0.18 0.82]
P^4 =
(Type an integer or decimal for each matrix element. Round to four decimal places as needed.)
Continue taking powers of P until S can be determined
S =
(Type an integer or decimal for each matrix element. Round to four decimal places as needed.)

S = [0.2069,0.7931]

Step-by-step explanation:

Transition Matrix:

Stationary matrix S for the transition matrix P is obtained by computing powers of the transition matrix P ( k powers ) until all the two rows of transition matrix p are equal or identical.

Transition matrix P raised to the power 2 (at k = 2)

Transition matrix P raised to the power 3 (at k = 3)

Transition matrix P raised to the power 4 (at k = 4)

Transition matrix P raised to the power 5 (at k = 5)

P⁵ at k = 5 both the rows identical. Hence the stationary matrix S is:

S = [ 0.2069 , 0.7931 ]

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.