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.
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The test suite has a bug with respect to the indexing of vector U(). If U(1) = a and U(2) = b, as in tests 1 and 2, then the indexing of U() in the subsequent tests are all off by 2. Essentially, U(3) and U(4) are missing from the series and are overwritten by U(1) and U(2).