Problem 58463. Recurssive serie

let the numerical serie U(n) such as U(n+1)= 0.2U(n) + 0.3U(n-1) ; U(0) = a ; U(1) = b
the goal is to plot the elements of this serie in a 2D graph after solving for the serie using matrix manipulation
Steps for solving : create the matrix
(0 1
0.3 0. 2)
Find the eigen values ,create a diagonal matrix using those eigen values
Find the matrix whose colomns are the eigen vectors
HINT ( there is only two eigen values. The first element of the diagonal matrix is the negative eigen value!)
Calculate the vector U for every n >=2 such as U(n) = x(2,1)*U(0) + X(2,2)*U(1)
HINT (the matrix X = P * D^n * P^-1 such as D is the diagonal eigen values matrix and P is the eigen vectors matrix.)
plot the vector U with n being the length of U, you don't need to round the values of the serie.
Solve

Solution Stats

85.71% Correct | 14.29% Incorrect
Last Solution submitted on Jun 28, 2023

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