Q1/Sketch the root locus for the system shown in Figure 1 and find the following: a. The exact point and gain where the locus crosses the jo-axis b. The breakaway point on the real axis c. The range of K within which the system is stable d. Angles of departure and arrival R(s) + K(s²-4s +20) C(s) (s+2)(s + 4)

Exam2 Subject: (Numerical Analysis) Class: Third Date: 27/4/2025 Time: 60 minutes Q1. For what values of k does this system of equations has no solution? (use Gauss-Jordan eliminations) kx + y + z = 1 x+ky + z = 1 x+y+kz=1

Consider the Difference equation of a causal Linear time-invariant (LTI) system given by: (y(n) - 1.5y(n - 1) + 0.5y(n = 2) = x(n) a) Implement the difference equation model of this system. b) Find the system transfer function H(z). c) For an input x(n) = 8(n), determine the output response y(n). d) Verify the initial value theorem y(0) with part (c).