Unformatted text preview: A ? (c) For a given u = ± 1-1 ² T , represent y in the form of the linear combi-nation of the eigenvectors of Matrix A . (d) Re-deﬁne a new set of input and output variables such that the input output relationship is decoupled (that is, there is no interactions between diﬀerent inputs). (e) Find the inverse mapping from y to u such that you can calculator corre-sponding u from given y . 3. For a given matrix A and its eigenvalues λ 1 , λ 2 . . . λ n , prove that the eigenvalues of A-1 would be 1 /λ 1 , 1 /λ 2 , . . . 1 /λ n if A-1 exists. 1...
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- Linear Algebra, state variables, input output relationship