Question

solve the system of linear recurrence relations:
x (n+1) = -x(n)+3y(n)
y(n+1) = -3x(n) +5y(n) with start up condition (x(0) =1 and y(0) =2. Anybody help me. the condition should be posted in attached part

Answer 1

with start up condition \[\left(\begin{matrix}_{xo} \\ yo\end{matrix}\right)=\left(\begin{matrix}1 \\ 2\end{matrix}\right)\]

Answer 2

make a matrix
find the eigen values and eigen vectors