Consider the system represented in state variable formVerify that the system is observable and controllable. If so, design a full-state feedback law and an observer by placing the closed-loop system poles at s_{1, 2} = -1 + j and the observer poles at s_{1, 2} = -12.

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where x(t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t), 2 2 [1²0] B [1] = -8 C = [52], and D= [0]. A