Apply the r-transform to the following characteristic equations of a discrete-data control system 2 3 2 ( .) 1.5 1 0 ( .) 2 0.5 0 i z z ii z z z        (a) determine the equivalent characteristic equations in r. (b) apply routh-hurwitz to determine how many roots of the characteristic equation are in the left half r-plane, in the right half r-plane, and on the imaginary axis. (c) use matlab or labview mathscript to determine the roots of the z and r characteristic equations and confirm your results in part (b). (use "roots" to solve for the root locations.)