The given matrix is an absorbing stochastic matrix in...

The given matrix is an absorbing stochastic matrix in standard form. Identify R and S and compute the fundamental matrix and the stable matrix.\\ $\begin{bmatrix} 1 & 0 & \frac{1}{5} & \frac{1}{10} \\ 0 & 1 & \frac{2}{5} & 0 \\ 0 & 0 & \frac{1}{5} & \frac{1}{5} \\ 0 & 0 & \frac{1}{5} & \frac{7}{10} \end{bmatrix}$

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00:01 Hi, here we are given the absorbing statistic matrix.

00:06 So the absorbing matrix it is 1 .0000, then we have 0 .3, 0 .3, 0 .1, 0 .3 and 0 .1 .2.

00:46 From here now if we divide this matrix, so that will be equivalent as this is i, this is zero matrix, then we get this matrix as r and this matrix as s.

01:09 Therefore, r will be equal to 0 .3 ,1, 0 .6 and 0 .2.

01:20 S matrix will be 0 .3 .3.

01:27 This will be 0 and point.

01:32 Further now we'll find the stable matrix.

01:36 So for that it can be said that consider i minus r.

01:48 The matrix that we get is 0 .7 minus 0 .1 minus 0 .6 and 0 .8.

01:57 I minus r inverse it will be equal to 1 divided by the determinant of this matrix that will be 0 .5 into 0 .8 0 .7 and signs of this will change 0 .6 and 0 .1 so that will be equal to we get this as we'll keep it like this that means 1 by 0 .5 into 1 by 0 .5 into 1.

02:32 To 0 .8, this is 0 .1, this is 0 .6, this is 0 .7.

02:40 So, further it can be said that s into i minus r inverse will be 1 divided by 0 .5 into 0 .3, 0 .3.

02:57 This will be 0 and 0 .2.

03:00 Into 0 .8, this is 0 .1, this is 0 .6 and 0 .7.

03:08 That is equal to 0 .48, 0 .48 .48.

03:15 This will be 0 .36 and 0 .36.

03:21 So therefore, the stable matrix, it will be 1 .000, this is 0 -1 -0 -0 -0 .000...

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