An unforced linear time invariant (LTI) system is represented by $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right].$$$

If the initial conditions are x₁(0)= 1 and x₂(0)=-1, the solution of the state equation is

Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is

In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms W₁, W₂, W₃ and W₄.

The outputs of the two flip-flops Q₁, Q₂ in the figure shown are initialized to 0, 0. The sequence generated at Q₁ upon application of clock signal is