I only need question 4, Thank you.In the presence of enough food and lacking predators and competitors, a population of rabbitswill increase by a fixed percentage each spring. For this set of exercises, we will say that therabbit population increases by 10% each year. Thus, if the initial population is R0, then thepopulation the following spring will be R1 = (1.1)R0 rabbits. In two years, the population will beR2 = (1.1)R1 = (1.1)2R0. The number of rabbits after n years will beRn = (1.1)nR0,and clearly the rabbit population grows without bound. We will assume that the rabbit populationis measured in hundreds of rabbits (so that R = 1 represents 100 rabbits).Suppose now that we introduce a small number of cougars into the environment to keep the rabbitpopulation under control.Let’s suppose that the amount of rabbits eaten each year is proportional to the cougar population.Then the change in the rabbit population is governed by the equationRn+1 = (1.1)Rn − (0.1)Cn,where Rn and Cn represent the rabbit and cougar populations in year n, respectively, rabbits measured in hundreds and cougars measured in singles. The constant 0.1 is the kill rate. If there are no cougars, what does the equation Rn+1 = (1.1)Rn - (0.1)Cn say about thechange in the population of rabbits? Does that make sense?The rate of growth of the cougar population will depend on both the number of cougars andthe number of rabbits. We will assume that the growth of the cougar population is governedby the equationCn+1 = (0.3) Rn+ (0.7)Cn.If there are no rabbits, what does the equation Cn+1 = (0.3)R₁ + (0.7)Cn say about thechange in the population of cougars? Does that make sense?We can combine these two equations into a system:Let A =1-0.1[0.300.7][Rn+11.1[+] = [0.3 -0.7] [²].Cn+1Is matrix A invertible? How do you know?Suppose that the initial populations of rabbits is 1000 and the initial population of cougarsis 2. Then we can represent the intial population byFind the population vector after a year. Round to whole numbers of animals (that is, roundthe value of R₁ to two decimal places and round the value of C₁ to an integer).

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Accepted Answer

4 QUESTION ANSWEr
|A|=ad -bc 
DetA not equal to zero so matrix inversion exists 
Cofactor of A=…

Let A = 1.1 0.3 -0.1 0.7 Is matrix A invertible? How do you know?