Section A
Q1.
(a)
Find the eigenvalues and the corresponding eigenvectors of the matrix \beginbmatrix 3 & -1 & -2 \ -1 & 3 & 2 \ -2 & 2 & 6 \endbmatrix.
Is this matrix diagonalizable? Justify your answer.
(b) Classify the ways in which materials respond to magnetic fields and also specify their value of susceptibility.
(c) The material parameters of a certain food item are given by σ = 2.2 s/m, \epsilon = 48\epsilon0 and μ = μ_0 at the operating frequency, f = 2.54 GHz of a microwave oven. Determine α, β, λ, vp and \overline\eta. Take \epsilon0 = (10-9)/(36π) and μ_0 = 4π × 10-7.
(d)
The following equations refer to a two-port network
V1 = 5I1 + 2I2
V2 = 2I1 + I2
A load resistance of 3 ohms is connected across port-2 terminals as shown in figure. Calculate the input Impedance.
(e) Write a program in any programming language to compute the money accumulated in a cumulative fixed deposit of a bank for the principal P after n years. The rate of interest is r percent per year compounded annually. The program should read the values of P, r and n. It should display the accumulated money as F.
