## Inequalities, vectors, matrix: olive oil research study

Hi everyone,

I have started studying in Barcelona Administration and management and I am struggling with a subject called "Fundamentals of Math" which I do not consider as "fundamentals" at all!

I need your help as I have stucked here...

Market research olive oil and seed oil of Spain, initially two markets are in equilibrium, but fierce campaign on the health benefits of olive oil consumption implied significant differences in the decisions of consumers. Such are the relations of changes

x k +1 = 0.4 + 0.5 yk xk
y k +1 = 0.2 + 0.1 yk xk

where xk and yk are changes in the market of olive oil and seed oil. Are these distortions going to disappear in the long run?

a) What is distortion when k = 1, if the initial changes in both markets at the k = 0 time were (x0, y0) = (0.3, 0.7)?

b) Find a diagonal matrix D formed by the eigenvalues ​​of the matrix A.

c) Find a matrix P with the change of the basis formed by the eigenvectors of A.

d) Taking into account the data from the study and analysis of the behavior of the matrix Ak for k values​​, it is expected that the distortion will disappear?

Note: Calculate \ lim_ {x \ to} \ infty Ak and analyze the results.

I will be very grateful for your help, you are my last resort....