If P = begin{bmatrix} 1 & 0 1/2 & 1 end{bmat | vedclass

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(B) Given $P = \begin{bmatrix} 1 & 0 \ 1/2 & 1 \end{bmatrix}$.Calculate $P^2 = P 	imes P = \begin{bmatrix} 1 & 0 \ 1/2 & 1 \end{bmatrix} \begin{bma

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$\begin{bmatrix} 1 & 0 \ 25 & 1 \end{bmatrix}$

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(B) Given $P = \begin{bmatrix} 1 & 0 \ 1/2 & 1 \end{bmatrix}$.Calculate $P^2 = P 	imes P = \begin{bmatrix} 1 & 0 \ 1/2 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \ 1/2 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 1/2 + 1/2 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 1 & 1 \end{bmatrix}$.Calculate $P^3 = P^2 	imes P = \begin{bmatrix} 1 & 0 \ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \ 1/2 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 1 + 1/2 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 3/2 & 1 \end{bmatrix}$.Calculate $P^4 = P^2 	imes P^2 = \begin{bmatrix} 1 & 0 \ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \ 1 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 1 + 1 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 2 & 1 \end{bmatrix}$.Observing the pattern,$P^n = \begin{bmatrix} 1 & 0 \ n/2 & 1 \end{bmatrix}$.Therefore,for $n = 50$,$P^{50} = \begin{bmatrix} 1 & 0 \ 50/2 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 25 & 1 \end{bmatrix}$.

If $P = \begin{bmatrix} 1 & 0 \\ 1/2 & 1 \end{bmatrix}$,then $P^{50}$ is:

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