The state model
\[\begin{array}{l} x\left( {k + 1} \right) = \left[ {\begin{array}{*{20}{c}} 0&1\\ { - \beta }&{ - \alpha } \end{array}} \right]x\left( k \right) + \left[ \begin{array}{l} 0\\ 1 \end{array} \right]u\left( k \right)\\ y\left( k \right) = \left[ {0\,\,\,1} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}&{\left( k \right)}\\ {{x_2}}&{\left( k \right)} \end{array}} \right] \end{array}\]
is represented in the difference equation as

A. y(k + 2) + αy(k + 1) + βy(k) = u(k)

B. y(k + 1) + αy(k) + βy(k - 1) = u(k)

C. y(k - 2) + αy(k - 1) +βy(k) = u(k)

D. y(k - 1) + αy(k) + βy(k + 1) = u(k + 1)

Answer: Option B