Reference no: EM13655568
1. Let
Using Matlab (each question below can be answered by one Matlab statement),
1) calculate bTb ;
2) calculate (b + jb)T AAT b ;
3) calculate bTA - (AT b)T
4) calculate (AT A)-1 A;
5) solve the equation AT Ax = c ;
6) solve the equation cr = xA T A ;
7) find the roots of f (s) ;
8) find the roots of f 2 (S) ;
9) find the roots of polynomial (s2 + 2)f (s) + 30 ;
10) find the roots of polynomial f2(s) + 5 f (s) + 1.
2. Count the number of positive values in a matrix 0.5-rand(5,6) and find out which element in the matrix has the largest value.
3. Write a program that use Matlab ‘function' to do the following calculations:
(a) the sum of all elements in a matrix;
(b) the mean of all negative elements in the first column of a matrix.
4. Write a program that will read in a text string mixed with numbers and letters from the keyboard and count how many numbers there are in the string.
5. Plot a 3D graphics described by the following equation:
i = 10sin(0.05ft)
where i is the current in ampere, the time t changes from 0 to 20 seconds and the frequency f can change from 10 to 15 Hz.
6. In the circuit below, if the resistor R4 changes from 0? to 40? in 0.2? steps and Vs changes from 4v to 24V in 0.1V steps, write a program to plot 3D graphics of the voltage on R2 against both the resistance of R4 and the voltage Vs using Matlab.
7. In the RLC series circuit below, Vm=240, f=50Hz, R=5?, L=4mH and C=1500µF. Write a program to plot 2D graphics of the current i against time t (from 0 to 0.04s with 0.001steps).
8. In the integrating amplifier circuit below, the input Vi=1.5sin(0.5πt), R1= 20?, C=0.02F. Write a program to plot the output Vo and input Vi against time t from 0 to 8s with 0.02s steps.
9. In the RLC network given below, assume that the input e(t) is a unit-step signal, C=0.0025F, R=2? and the inductance L changes from 0H to 0.3H with 0.03H steps. Write a program to display all unit-step responses of the capacitor's voltage Vc for different inductance L in a 2D diagram.
