Linear Algebra Question A county is divided into three regio

Linear Algebra Question:

A county is divided into three regions. Each year, 10% of the residents of region 1 move to region 2 and 5% move to region 3; 15% of the residents of region 2 move to region 1 and 5% move to region 3; and 10% of the residents of region 3 move to region 1 and 10% move to region 2. This year the total population of the county is 426,750. Use eigenvalues and eigenvalues to find the steady state matrix for the populations.

(I am guessing he meant eigenvalues and eigenvectors to find the steady state matrix for the populations)

Solution