(20pts) Consider the state-space system x = [+ 1 2] + [ ] u, y =...

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(20pts) Consider the state-space system x = [+ 1 2] + [ ] u, y = [1_1]X [] (a) (12pts) Determine the solution of X(t) for the initial condition X(0) = [1] a input. Hint: The use of Laplace Transforms is recommended. (b) (8pts) Determine the transfer function between u(s) and y(s). and a unit step (20pts) Consider the state-space system x = [+ 1 2] + [ ] u, y = [1_1]X [] (a) (12pts) Determine the solution of X(t) for the initial condition X(0) = [1] a input. Hint: The use of Laplace Transforms is recommended. (b) (8pts) Determine the transfer function between u(s) and y(s). and a unit step