Answer
See solution
Work Step by Step
a) $x_0=\begin{bmatrix}
38,041,430\\275,872,610
\end{bmatrix}$
$\frac{748,252}{38,041,430}=0.01967$ fraction of the people in California went outside California and $1-\frac{748,252}{38,041,430}=0.98033$ fraction remained.
Similarly, $\frac{493,641}{275,872,610}=0.00179$ fraction of the people outside California went inside California and $1-\frac{493,641}{275,872,610}=0.99821$ fraction of the people outside California remained outside California.
Thus, the migration matrix is $M=\begin{bmatrix}
0.98033&0.00179 \\0.01967&0.99821
\end{bmatrix}$
b) $x_{10}=\begin{bmatrix}
0.98033&0.00179 \\0.01967&0.99821
\end{bmatrix}^{10}\begin{bmatrix}
38,041,430\\275,872,610
\end{bmatrix}=\begin{bmatrix}
35,727,629\\278,186,410
\end{bmatrix}$
