If data A and B are the initial market shares of R company and S company, then a+b = 1. In order to keep the future market distribution unchanged, according to the law of customer number transfer, there are: 1434 13A = 2bb3, that is, 343413a = 01b.

If the equation has a solution, we should choose a positive solution from the set of non-zero solutions as the initial share, program and calculation result of market stability, so as to get the market distribution after two years, five years and ten years.

a =[ 1/4 1/3； 3/4 2/3]% input transfer matrix

A & gt& gtx0 =[3/5； 2/5]% Enter the initial vector, that is, the initial market share.

& gt& gtX2 = a 2 * x0% Calculate the market share after two years.

& gt& gtX5 = a 5 * x0% Calculate the market share after five years.

& gt>x10 = a10 * x0% to calculate the market share after ten years.

x2 = 0.3097 0.6903 x5 = 0.3077 0.6923

concept

Linear algebra is a branch of algebra, which mainly deals with linear relations. Linear relationship means that the relationship between mathematical objects is expressed in linear form. For example, in analytic geometry, the equation of a straight line on the plane is a binary linear equation; The equation of spatial plane is a ternary linear equation, and the spatial straight line is regarded as the intersection of two planes, which is represented by an equation group composed of two ternary linear equations.

A linear equation with n unknowns is called a linear equation. Functions whose variables are linear are called linear functions. Linear relation problem is called linear problem for short. The problem of solving linear equations is the simplest linear problem.