Exercise 1:

Let

A = 250/I+100

and

T = 1/ 5I

For the expressions for a_n and b_n, use MATLAB to plot the function

for values of N = 5, 10, 20, for the time interval 0 ≤ t ≤ T. Plot the original periodic square wave on the same graph. Comment on the difference between the original periodic square wave and its truncated Fourier series presentation.

Exercise 2:

Use MATLAB to plot the periodic square wave 5 f(t) over the time interval 0 ≤ t ≤ 3T  . On the same graph, plot the output waveforms, f₀(t), of the two amplifiers with corner frequencies of F =  10I and F = 40I, respectively. Comment on the plots.

Exercise 3:

Matrix A and vector b are defined by

(a) Solve the linear system of equations Ax = b using MATLAB.

(b) Find A^{-1 }and verify that A^-1 A = I, where I is the 6X6 identity matrix. Compute x = A^-1b using MATLAB and check the result with that of (a).
(c) Compute the determinant of A.

(d) Take matrix A' as A' = A + A^T, where A^T is the transpose of A . Using MATLAB, solve the linear system of equations A'x = b.

(e) Take matrix S as

Compute the rank of S manually and use the MATLAB function to verify the result.