Problem 1 (Problem 2.10-4 from the textbook) Consider the system described by x(k + 1) = 1 0 x(k) + 0 0.5 2 k) 1 y(k) = [ 1 2 ]x(*) (a) Find the transfer function Y(z)/U (z). (b)Using any similarity...

I need help with subparts  b, c, d. Thanks!

Extracted text: Problem 1 (Problem 2.10-4 from the textbook) Consider the system described by x(k + 1) = 1 0 x(k) + 0 0.5 2 k) 1 y(k) = [ 1 2 ]x(*) (a) Find the transfer function Y(z)/U (z). (b)Using any similarity transformation, find a different state model for this system. (c) Find the transfer function of the system from the transformed state equations. (d)Verify that A given and A, derived in part (b) satisfy the first three properties of similarity transformations. The fourth property was verified in part (c).