Practice FT1 Q8 - Looking for a detailed, worked solution with theoretical explanation

Two bank accounts are opened simultaneously. We call them account X and acount Y. Account X starts with 200,000 dollars and earn 3 % interest per annum. At the end of each year the interest is paid into account X. Account Y starts with 300,000 dollars and earns 5 % interest per annum. At the end of each year, half the interest is paid into account X and half into account Y. Let In and yn be the amount of money (in dollars) in X and Y respectively at the end of n years, including the nth interest payment. Write vn = a) Find a matrix A such that Vn+1 = Avn for all non-negative integers n. Enter the matrix A in the box below. Insert matrix result Explain briefly in the box below how you obtain the above matrix A. Insert explanation b) Find an invertible matrix M and a diagonal matrix D such that A = MDM -1, and " " ) . , where a > b . Enter the values of a and b in the boxes below. a = Number b = Number Enter the matrix M in the box below. Insert matrix result Explain briefly how do you obtain the answers in this part, part (iii), in the box below. Insert explanation c) After 10 years, the amount of money in dollars in account X is Number to the nearest $1000; account Y is Number to the nearest $1000. Explain briefly how do you obtain the answers in this part, part (iii), in the box below. Insert explanation