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 } 1 & 0 \\0.4 & 0.6\end{array} \right]

v = \left[ \begin{array} { l l } 0.6 & 0.4\end{array} \right]

A)The two-step transition matrix is

\left[ \begin{array} { c c } 1 & 0 \\0.64 & 0.36\end{array} \right]

The distribution vector is

\left[ \begin{array} { l l } 0.856 & 0.144\end{array} \right]

B) The two-step transition matrix is

\left[ \begin{array} { c c } 1 & 0 \\0.64 & 0.36\end{array} \right]

The distribution vector is

\left[ \begin{array} { l l } 0.16 & 0\end{array} \right]

C) The two-step transition matrix is

\left[ \begin{array} { c c } 1 & 0 \\0.64 & 0.36\end{array} \right]

The distribution vector is

\left[ \begin{array} { l l } 1 & 0\end{array} \right]

D) The two-step transition matrix is

\left[ \begin{array} { c c } 0.64 & 0.36 \\1 & 0\end{array} \right]

The distribution vector is

\left[ \begin{array} { l l } 0 & 1\end{array} \right]

E) The two-step transition matrix is

\left[ \begin{array} { l l } 0.16 & 0.36 \\0.64 & 0.36\end{array} \right]

The distribution vector is

\left[ \begin{array} { l l } 0.856 & 0.144\end{array} \right]

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