Use the Given Transition Matrix P and the Given Initial $P = \left[ \begin{array} { c c } 0.9 & 0.1 \\0 & 1\end{array} \right]$

Multiple Choice

Use the given transition matrix P and the given initial distribution vector v to obtain the two-step transition matrix and the distribution vector after two steps. $P = \left[ \begin{array} { c c } 0.9 & 0.1 \\0 & 1\end{array} \right]$ , $v = \left[ \begin{array} { l l } 0.9 & 0.1\end{array} \right]$

A) The two-step transition matrix is $\left[ \begin{array} { c c } 0.81 & 0.19 \\0 & 1\end{array} \right]$ The distribution vector is $\left[ \begin{array} { l l } 1 & 0\end{array} \right]$
B) The two-step transition matrix is $\left[ \begin{array} { c c } 0 & 1 \\0.81 & 0.19\end{array} \right]$
The distribution vector is $\left[ \begin{array} { l l } 0 & 1\end{array} \right]$
C) The two-step transition matrix is $\left[ \begin{array} { c c } 0.81 & 0.01 \\0 & 1\end{array} \right]$
The distribution vector is $\left[ \begin{array} { l l } 0.729 & 0.271\end{array} \right]$
D) The two-step transition matrix is $\left[ \begin{array} { c c } 0.81 & 0.19 \\0 & 1\end{array} \right]$
The distribution vector is $\left[ \begin{array} { l l } 0.81 & 0\end{array} \right]$
E) The two-step transition matrix is $\left[ \begin{array} { c c } 0.81 & 0.19 \\0 & 1\end{array} \right]$
The distribution vector is $\left[ \begin{array} { l l } 0.729 & 0.271\end{array} \right]$