Solve the system of equations using the matlab functions or

Question

Questions

1. Evaluate the following mathematical expression using MATLAB commands. Display your results by omitting semicolons at the end of your command lines.

1/⁴√5²+ 6^2/3;

R = (8x³√x + 5^1/3x²)/x√x+4^1/3x^2/3

where x = ³√(200 - 4√2 + 3(√99 - 3√5))

2. Solve the following system of equations using the MATLAB functions or operators:

2x-y+3z-t -3

x-2y-2z-3t = 2

5x -3y- z +2t = 3

3x-Fy+z+4t=7

Verify your solution using matrix multiplication.

3 Input the matrices

(a) Using MATLAB functions, verify that det(A) det(B) = det(AB) ;

(b) Calculate AB and 3A^TB^-1- 3B.

4 Write a MATLAB script to produce the graphs of the functions y₁ = 2x-2 , y₂ = x² - 2 + 2 and y₃ = -x³ in the range of -3:0.013 using the same axes. Use the MATLAB functions xlabel, ylabel.legend and title to annotate your graph clearly.

5. Use the surf function to plot z = x²/(1+y²), for, =-5:01 :5 and y =-5:0.1:5.

6. Write a MATLAB script to plot the piece-wise function of given by:

f(x) = 3x² - Π²/4
f(x) = 4cosx + Π²  -Π/2 ≤ x ≤ Π/2
f(x) = x² + Π²/4    x < -Π/2

x varies between -Π and Π with 100 data points.

7. For x = 1:10 calculate y = e^0.2x, use fopen and fprintf to write x and y data into a file named "my ex_data . dat". Then use fopen and fscanf to read the x and y data. Show the data in 2 columns.

8. Write a MATLAB code using the switch statement to show whether a day of the week is a week day or weekend day. The day of the week is read in from the user as a string. Monday, through Friday are assumed to be week days and Saturday and Sunday are assumed to be weekend days.

9. We know that 1 - 1/3 + 1/5 -1/7 + = 1/4Π. How many terms do we need to have in order for the error to be smaller than 10^-4? Write a MATLAB code to find out.

10. Write a MATLAB program that will display the numbers from 1 to 1000 which are cubic numbers (such as 8 = 2*2*2). The program should display: 1, 8, 27, .... Run your program and verify that it operates correctly.