Two colonies of ants have been observed engaging in an ant war with each other. The population of ants in thefirst colony can be modelled using the discrete dynamical systemYn+1[an+1]=Awhere yn is the population of young ants in the colony after n weeks, an is the population of adult ants in thecolony after n weeks, and A is a 2 by 2 matrix.O 10YnanSuppose A has 0.5 as an eigenvalue, with a corresponding eigenvector× H[3].Initially when the ant war started, the populations are given by yoO 152a corresponding eigenvectorO 20-and 1 as its other eigenvalue, with:30 and aoHow many young ants does the model predict will be in the first colony after 2 weeks?Select one alternative:05=70.

We need to diagonalize the matrix A in order to get the solution of given discrete dynamical system.…

Two colonies of ants have been observed engaging in an ant war with each other. The population of ants in the first colony can be modelled using the discrete dynamical system Yn+1 [2+1] = A[], [an+1_ where yn is the population of young ants in the colony after ŉ weeks, an is the population of adult ants in the colony after n weeks, and A is a 2 by 2 matrix. Suppose A has 0.5 as an eigenvalue, with a corresponding eigenvector a corresponding eigenvector 3 Initially when the ant war started, the populations are given by yo = O 10 and ao How many young ants does the model predict will be in the first colony after 2 weeks? Select one alternative: 0 5 O 15 [2]. " O 20 and 1 as its other eigenvalue, with 70.