Suppose A is a 4 x 4 matrix and B is a 4 x 2 matrix, and let uo, ..., U3 represent a sequence of input vectors in R 2 a. Set Xo = 0, compute X1,..., X4 from equation (1), and write a formula for x4 involving the controllability matrix M appearing in equation (2). (Note: The matrix M is constructed as a partitioned matrix. Its overall size here is 4 x 8.) %3D b. Suppose (A, B) is controllable and v is any vector in R4. Explain why there exists a control sequence uo, ..., U3 in TR 2 such that x4 = v.

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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