- #1

- 634

- 15

For a 2 x 2 matrix ##A## representing a Markov transitional probability, we can compute the stationary vector ##x## from the relation $$Ax=x$$

But can we compute ##A## of the 2x2 matrix if we know the stationary vector ##x##?

The matrix has 4 unknowns we should have 4 equations;

so for a ##A = \begin{bmatrix}

a & b \\

c & d

\end{bmatrix}## , we got

$$

\begin{bmatrix}

a & b \\

c & d

\end{bmatrix}

\begin{bmatrix}

\alpha\\

\beta

\end{bmatrix}=

\begin{bmatrix}

\alpha\\

\beta

\end{bmatrix}

$$

The system of 4 equations;

$$\alpha a+\beta b=\alpha, \alpha c +\beta d=\beta, a+c=1, b+d=1 $$

Given that ##\alpha## and ##\beta## are known.