Power of a matrix - Your turn

Suppose each year, \(5\%\) of the students at UC Berkeley transfer to Stanford and \(1\%\) of the students at Stanford transfer to Berkeley. Determine the population after \(5\) years if there were initially \(50,000\) students at Berkeley and \(10,000\) students at Stanford. The transformation matrix to use is \(A = \begin{bmatrix} 0.99 & 0.05 \\ 0.01 & 0.95 \end{bmatrix}\).

Note

\(x_1\) is the Stanford population and \(x_2\) is the Berkeley population.

# TODO: Write your solution below

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