Calculus Level pending

A discrete-time system is described by the state equation

$V(k+1) = A V(k) + B u$

with $$V(k) = [ x(k) , y(k) ]^T$$ being the state vector, and

$A = \begin{bmatrix} 2 && -3 \\ 0.5 && -0.5 \end{bmatrix}$

$B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$

$u = 1$

If the system is initially relaxed, i.e. $$V(0) = [ 0 , 0 ]^T$$, then what is the value of the following limit

$\lim_{k \to\infty} \frac{x(k)}{y(k)}$

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